{"id":20417,"date":"2026-01-18T23:24:30","date_gmt":"2026-01-18T17:54:30","guid":{"rendered":"https:\/\/www.geographynotespdf.com\/?p=20417"},"modified":"2026-04-08T20:13:37","modified_gmt":"2026-04-08T14:43:37","slug":"mean-deviation","status":"publish","type":"post","link":"https:\/\/geographynotespdf.com\/cms\/mean-deviation\/","title":{"rendered":"2. Mean Deviation (\u0914\u0938\u0924 \u0935\u093f\u091a\u0932\u0928)"},"content":{"rendered":"\n\n\n
\n

Mean Deviation <\/strong><\/span><\/h2>\n

(\u0914\u0938\u0924 \u0935\u093f\u091a\u0932\u0928)<\/strong><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"Mean<\/h3>\n

Definition \/ \u092a\u0930\u093f\u092d\u093e\u0937\u093e<\/strong><\/span><\/h3>\n

\u00a0 \u00a0 \u00a0 Mean Deviation is a statistical measure of dispersion which is calculated as the average of absolute deviations of observations from a central value (Mean, Median or Mode).<\/span><\/strong><\/span><\/p>\n

\u00a0 \u00a0 \u0914\u0938\u0924 \u0935\u093f\u091a\u0932\u0928 \u0935\u0939 \u092a\u094d\u0930\u0938\u093e\u0930 \u092e\u093e\u092a \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 \u0938\u092d\u0940 \u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0923\u094b\u0902 \u0915\u0947 \u0915\u093f\u0938\u0940 \u0915\u0947\u0902\u0926\u094d\u0930\u0940\u092f \u092e\u093e\u0928 (\u092e\u093e\u0927\u094d\u092f, \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e \u092f\u093e \u092c\u0939\u0941\u0932\u0915) \u0938\u0947 \u092a\u0930\u092e \u0935\u093f\u091a\u0932\u0928\u094b\u0902 \u0915\u093e \u0914\u0938\u0924 \u0928\u093f\u0915\u093e\u0932\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/strong><\/span><\/p>\n

✍️ <\/strong>\u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0915\u0940 \u0917\u0923\u0928\u093e \u092e\u0947\u0902 \u0938\u092d\u0940 \u0935\u093f\u091a\u0932\u0928\u094b\u0902 \u0915\u094b \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u092e\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0926\u0942\u0938\u0930\u0947 \u0936\u092c\u094d\u0926\u094b\u0902 \u092e\u0947\u0902, \u0935\u093f\u091a\u0932\u0928\u094b\u0902 \u0915\u0947 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091a\u093f\u0939\u094d\u0928 ‘+’ \u0924\u0925\u093e ‘-‘ (\u0927\u0928 \u0924\u0925\u093e \u090b\u0923) \u0915\u0940 \u0909\u092a\u0947\u0915\u094d\u0937\u093e \u0915\u0930\u0915\u0947 \u0938\u092d\u0940 \u0935\u093f\u091a\u0932\u0928\u094b\u0902 \u0915\u094b \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u092e\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0905\u0930\u094d\u0925\u093e\u0924\u094d ‘\u0928\u093f\u0930\u092a\u0947\u0915\u094d\u0937 \u0935\u093f\u091a\u0932\u0928’ (absolute deviation) \u091c\u094d\u091e\u093e\u0924 \u0915\u093f\u092f\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 <\/span><\/p>\n

✍️ <\/strong>\u091a\u093f\u0939\u094d\u0928\u094b\u0902 \u0915\u094b \u091b\u094b\u0921\u093c\u0928\u0947 \u0915\u093e \u0915\u093e\u0930\u0923 \u092f\u0939 \u0939\u0948 \u0915\u093f \u092e\u093e\u0927\u094d\u092f \u0938\u0947 \u0928\u093f\u0915\u093e\u0932\u0947 \u0917\u092f\u0947 \u0935\u093f\u091a\u0932\u0928\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \u0936\u0942\u0928\u094d\u092f \u0924\u0925\u093e \u0905\u0928\u094d\u092f \u092e\u093e\u0927\u094d\u092f\u094b\u0902 \u0938\u0947 \u0928\u093f\u0915\u093e\u0932\u0947 \u0917\u092f\u0947 \u0935\u093f\u091a\u0932\u0928\u094b\u0902 \u0915\u093e \u092f\u094b\u0917, \u092f\u0926\u093f \u0935\u093f\u0924\u0930\u0923 \u092e\u093e\u092e\u0942\u0932\u0940 \u0905\u0938\u0902\u092e\u093f\u0924\u0940\u092f \u0939\u094b, \u0932\u0917\u092d\u0917 \u0936\u0942\u0928\u094d\u092f \u0939\u094b\u0924\u093e \u0939\u0948\u0964 <\/span><\/p>\n

\u00a0 \u00a0 \u00a0\u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0928\u093f\u092e\u094d\u0928 \u092c\u093e\u0924\u094b\u0902 \u0915\u093e \u0927\u094d\u092f\u093e\u0928 \u0930\u0916\u093e \u091c\u093e\u0924\u093e \u0939\u0948:-<\/span><\/p>\n

(1) \u092e\u093e\u0927\u094d\u092f \u0915\u093e \u091a\u0941\u0928\u093e\u0935:-<\/strong><\/span><\/p>\n

\u00a0 \u00a0 \u0938\u0948\u0926\u094d\u0927\u093e\u0928\u094d\u0924\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0915\u093f\u0938\u0940 \u092d\u0940 \u092e\u093e\u0927\u094d\u092f (\u092e\u093e\u0927\u094d\u092f, \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e \u0905\u0925\u0935\u093e \u092c\u0939\u0941\u0932\u0915) \u0938\u0947 \u0928\u093f\u0915\u093e\u0932\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u092a\u0930\u0928\u094d\u0924\u0941 \u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u092e\u0947\u0902 \u092e\u093e\u0927\u094d\u092f \u0924\u0925\u093e \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e \u0938\u0947 \u0939\u0940 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0915\u0940 \u092e\u093e\u092a \u091c\u094d\u091e\u093e\u0924 \u0915\u094b \u091c\u093e\u0924\u0940 \u0939\u0948\u0964<\/span><\/p>\n

(ii) \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091a\u093f\u0939\u094d\u0928\u094b\u0902 \u0915\u0940 \u0909\u092a\u0947\u0915\u094d\u0937\u093e:-<\/span><\/strong><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0935\u093f\u091a\u0932\u0928\u094b\u0902 \u0915\u0947 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091a\u093f\u0939\u094d\u0928\u094b\u0902 (\u0927\u0928 \u0935 \u090b\u0923) \u0915\u0940 \u0909\u092a\u0947\u0915\u094d\u0937\u093e \u0915\u0930\u0915\u0947 \u0938\u092d\u0940 \u0935\u093f\u091a\u0932\u0928\u094b\u0902 \u0915\u094b \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u092e\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u0935\u093f\u091a\u0932\u0928\u094b\u0902 \u0915\u094b \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f ‘d’ (deviation) \u0915\u0947 \u0926\u094b\u0928\u094b\u0902 \u0913\u0930 \u0938\u0940\u0927\u0940 \u0916\u0921\u093c\u0940 \u0930\u0947\u0916\u093e\u090f\u0901 \u092c\u0928\u093e \u0926\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948 \u0924\u0925\u093e |d| \u0932\u093f\u0916\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u0938\u0902\u0915\u0947\u0924\u093e\u0915\u094d\u0937\u0930 \u0915\u094b ‘mod d’ \u092a\u0941\u0915\u093e\u0930\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0938\u0947 \u0906\u0936\u092f ‘\u0928\u093f\u0930\u092a\u0947\u0915\u094d\u0937 \u0935\u093f\u091a\u0932\u0928’ (absolute deviation) \u0938\u0947 \u0939\u0948, \u0905\u0930\u094d\u0925\u093e\u0924\u094d \u0935\u093f\u091a\u0932\u0928 \u092e\u0947\u0902 ‘+’\u0905\u0925\u0935\u093e ‘-‘ \u0915\u094b \u0927\u094d\u092f\u093e\u0928 \u092e\u0947\u0902 \u0928\u0939\u0940\u0902 \u0930\u0916\u093e \u0917\u092f\u093e \u0939\u0948\u0964<\/span><\/p>\n

(iii) \u0935\u093f\u091a\u0932\u0928\u094b\u0902 \u0915\u093e \u092e\u093e\u0927\u094d\u092f \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u093e:- <\/span><\/strong><\/span><\/p>\n

\u00a0 \u00a0 \u0938\u092d\u0940 \u0928\u093f\u0930\u092a\u0947\u0915\u094d\u0937 \u0935\u093f\u091a\u0932\u0928\u094b\u0902 \u0915\u094b \u091b\u094b\u0921\u093c\u0915\u0930 \u092a\u0926\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e (N) \u0938\u0947 \u092d\u093e\u0917 \u0926\u0947\u0928\u0947 \u092a\u0930 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u091c\u094d\u091e\u093e\u0924 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

(iv) \u0938\u0902\u0915\u0947\u0924\u093e\u0915\u094d\u0937\u0930:-<\/span><\/strong><\/span><\/p>\n

\u00a0 \u00a0\u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0915\u0947 \u0938\u0902\u0915\u0947\u0924\u093e\u0915\u094d\u0937\u0930 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0917\u094d\u0930\u0940\u0915 \u0935\u0930\u094d\u0923\u092e\u093e\u0932\u093e \u0915\u093e \u0905\u0915\u094d\u0937\u0930 \u0921\u0947\u0932\u094d\u091f\u093e (Small Delta-‘\u03b4’) \u0915\u093e \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u091c\u094d\u091e\u093e\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0909\u0938\u0947 \u03b4 \u0915\u0947 \u0938\u093e\u0925 \u0909\u092a\u0938\u0902\u0915\u0947\u0924 (subscript) \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0932\u093f\u0916\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/span><\/p>\n

\u03b4x\u0304 <\/sub>= \u092e\u093e\u0927\u094d\u092f \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 <\/span><\/strong><\/p>\n

(Mean Deviation from Mean)<\/span><\/strong><\/p>\n

\u03b4M<\/sub> = \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928<\/span><\/strong><\/p>\n

(Mean Deviation from Median)<\/span><\/strong><\/p>\n

\u03b4Z<\/sub> = \u092c\u0939\u0941\u0932\u0915 \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 <\/span><\/strong><\/p>\n

(Mean Deviation from Mode)<\/span><\/strong><\/p>\n

\u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0917\u0941\u0923\u093e\u0902\u0915 <\/strong><\/span><\/h3>\n

(Co-efficient of Mean Deviation)<\/strong><\/span><\/p>\n

\u00a0 \u00a0 Coefficient of Mean Deviation is a relative measure of dispersion obtained by dividing Mean Deviation by the corresponding central value (Mean, Median or Mode). \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0917\u0941\u0923\u093e\u0902\u0915 \u0905\u092a\u0915\u093f\u0930\u0923 \u0915\u093e \u0938\u093e\u092a\u0947\u0915\u094d\u0937 \u092e\u093e\u092a \u0939\u0948, \u091c\u093f\u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0915\u094b \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0915\u0947\u0902\u0926\u094d\u0930\u0940\u092f \u092e\u093e\u0928 \u0938\u0947 \u092d\u093e\u0917 \u0926\u0947\u0915\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

Coefficient of Mean Deviation (CMD) = <\/span><\/span><\/span>MD \/ A (or MD\u0304 \/ A)<\/span><\/strong><\/p>\n

Where \/ \u091c\u0939\u093e\u0901,<\/strong><\/span><\/p>\n

MD = Mean Deviation<\/span><\/p>\n

A = Central Value (Mean \/ Median \/ Mode)<\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

(i) \u092e\u093e\u0927\u094d\u092f \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0915\u093e \u0917\u0941\u0923\u093e\u0902\u0915<\/span><\/strong><\/span><\/p>\n

(Co-efficient of Mean Deviation from Mean)<\/span><\/strong><\/span><\/p>\n

Coefficient of Mean Deviation\u00a0<\/span><\/span><\/span><\/strong><\/span><\/p>\n

= <\/span><\/span>Mean Deviation from<\/span>\u00a0Mean \/ Mean<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/strong><\/span><\/p>\n

(ii) \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0917\u0941\u0923\u093e\u0902\u0915<\/span><\/strong><\/span><\/p>\n

(Co-efficient of Mean Deviation from Median)<\/span><\/strong><\/span><\/p>\n

Coefficient of Mean Deviation\u00a0<\/span><\/span><\/span><\/strong><\/span><\/p>\n

= <\/span><\/span>Mean Deviation from\u00a0Median \/ Median<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/strong><\/span><\/p>\n

(iii) \u092c\u0939\u0941\u0932\u0915 \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0917\u0941\u0923\u093e\u0902\u0915<\/span><\/strong><\/span><\/p>\n

(Co-efficient of Mean Deviation from Mode)<\/span><\/strong><\/span><\/p>\n

Coefficient of Mean Deviation\u00a0<\/span><\/span><\/span><\/strong><\/span><\/p>\n

= <\/span><\/span>Mean Deviation from\u00a0Mode\u00a0\/ Mode<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/strong><\/span><\/p>\n

Why Coefficient is Used?<\/span><\/strong><\/p>\n

(\u0917\u0941\u0923\u093e\u0902\u0915 \u0915\u093e \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u094d\u092f\u094b\u0902?)<\/span><\/strong><\/p>\n

✍️ <\/strong>It removes the effect of units<\/span><\/p>\n

(\u092e\u093e\u092a \u0915\u0940 \u0907\u0915\u093e\u0908 \u0915\u093e \u092a\u094d\u0930\u092d\u093e\u0935 \u0938\u092e\u093e\u092a\u094d\u0924 \u0915\u0930\u0924\u093e \u0939\u0948)<\/span><\/p>\n

✍️ <\/strong>Helps in comparison of two or more distributions<\/span><\/p>\n

(\u0926\u094b \u092f\u093e \u0905\u0927\u093f\u0915 \u0935\u093f\u0924\u0930\u0923\u094b\u0902 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u092e\u0947\u0902 \u0938\u0939\u093e\u092f\u0915)<\/span><\/p>\n

Merits \/ \u0917\u0941\u0923<\/strong><\/span><\/p>\n

✍️ <\/strong>Simple to calculate (\u0917\u0923\u0928\u093e \u092e\u0947\u0902 \u0938\u0930\u0932)<\/span><\/p>\n

✍️ <\/strong>Useful for comparison (\u0924\u0941\u0932\u0928\u093e \u092e\u0947\u0902 \u0909\u092a\u092f\u094b\u0917\u0940)<\/span><\/p>\n

✍️ <\/strong>Easy to understand (\u0938\u092e\u091d\u0928\u0947 \u092e\u0947\u0902 \u0906\u0938\u093e\u0928)<\/span><\/p>\n

Demerits \/ \u0926\u094b\u0937<\/strong><\/span><\/h2>\n

✍️ <\/strong>Limited use in advanced statistics <\/span><\/p>\n

(\u0909\u0928\u094d\u0928\u0924 \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940 \u092e\u0947\u0902 \u0938\u0940\u092e\u093f\u0924 \u0909\u092a\u092f\u094b\u0917)<\/span><\/p>\n

✍️ <\/strong>Ignores algebraic signs<\/span><\/p>\n

(\u092c\u0940\u091c\u0940\u092f \u091a\u093f\u0939\u094d\u0928\u094b\u0902 \u0915\u0940 \u0909\u092a\u0947\u0915\u094d\u0937\u093e \u0915\u0930\u0924\u093e \u0939\u0948)<\/span><\/p>\n

\u0909\u092a\u092f\u094b\u0917 (Uses)<\/strong><\/span><\/h3>\n

✍️ <\/strong>\u0906\u092f, \u0935\u0947\u0924\u0928, \u0935\u0930\u094d\u0937\u093e, \u0924\u093e\u092a\u092e\u093e\u0928 \u0906\u0926\u093f \u0915\u0947 \u092a\u094d\u0930\u0938\u093e\u0930 \u0915\u0947 \u0905\u0927\u094d\u092f\u092f\u0928 \u092e\u0947\u0902<\/span><\/p>\n

✍️ <\/strong>\u0926\u094b \u092f\u093e \u0905\u0927\u093f\u0915 \u0935\u093f\u0924\u0930\u0923\u094b\u0902 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u092e\u0947\u0902<\/span><\/p>\n

\u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0935 \u0909\u0938\u0915\u0947 \u0917\u0941\u0923\u093e\u0902\u0915 \u0915\u0940 \u0917\u0923\u0928\u093e<\/strong><\/span><\/p>\n

(Computation of Mean Deviation and its Co-efficient)<\/strong><\/span><\/p>\n

\u0928\u094b\u091f:<\/span><\/strong><\/p>\n

\u00a0 \u00a0 Coefficient of Mean Deviation from Median<\/strong> is considered most appropriate<\/strong>. \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0917\u0941\u0923\u093e\u0902\u0915<\/strong> \u0938\u092c\u0938\u0947 \u0909\u092a\u092f\u0941\u0915\u094d\u0924 \u092e\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092f\u0939 \u091a\u0930\u092e \u092e\u093e\u0928\u094b\u0902 \u0938\u0947 \u0915\u092e \u092a\u094d\u0930\u092d\u093e\u0935\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

(i) \u0935\u094d\u092f\u0915\u094d\u0924\u093f\u0917\u0924 \u0936\u094d\u0930\u0947\u0923\u0940 (Individual Series)<\/strong><\/span><\/p>\n

\u00a0 \u00a0 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0915\u0940 \u0917\u0923\u0928\u093e \u092a\u094d\u0930\u0924\u094d\u092f\u0915\u094d\u0937 \u0930\u0940\u0924\u093f \u0938\u0947 \u0905\u0925\u0935\u093e \u0932\u0918\u0941 \u0930\u0940\u0924\u093f \u0938\u0947 \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948:-<\/span><\/p>\n

\u092a\u094d\u0930\u0924\u094d\u092f\u0915\u094d\u0937 \u0930\u0940\u0924\u093f (Direct Method)- <\/span><\/strong><\/p>\n

\u00a0 \u00a0 \u090f\u0915 \u0935\u094d\u092f\u0915\u094d\u0924\u093f\u0917\u0924 \u0936\u094d\u0930\u0947\u0923\u0940 \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u094d\u092f\u0915\u094d\u0937 \u0930\u0940\u0924\u093f \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901 \u0915\u0930\u0928\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948:-<\/span><\/p>\n

(i) \u092a\u0939\u0932\u0947 \u092e\u093e\u0927\u094d\u092f \u092f\u093e \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e \u092f\u093e \u092c\u0939\u0941\u0932\u0915, \u091c\u093f\u0938\u0938\u0947 \u092d\u0940 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0928\u093f\u0915\u093e\u0932\u0928\u093e \u0939\u094b, \u091c\u094d\u091e\u093e\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 <\/span><\/p>\n

(ii) \u0938\u092e\u094d\u092c\u0928\u094d\u0927\u093f\u0924 \u092e\u093e\u0927\u094d\u092f \u0938\u0947 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u092e\u0942\u0932\u094d\u092f\u094b\u0902 \u0915\u0947 \u0928\u093f\u0930\u092a\u0947\u0915\u094d\u0937 \u0935\u093f\u091a\u0932\u0928 |d| \u091c\u094d\u091e\u093e\u0924 \u0915\u093f\u092f\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 <\/span><\/p>\n

(iii) \u0928\u093f\u0930\u092a\u0947\u0915\u094d\u0937 \u0935\u093f\u091a\u0932\u0928\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \u2211|d| \u091c\u094d\u091e\u093e\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 <\/span><\/p>\n

(iv) \u2211|d| \u092e\u0947\u0902 \u092a\u0926 \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u0947 \u092d\u093e\u0917 \u0926\u0947\u0915\u0930 ‘\u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928’ \u091c\u094d\u091e\u093e\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964\u00a0<\/span><\/p>\n

\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930<\/span><\/p>\n

✍️ \u03b4x\u0304 <\/sub>= \u2211|x-x\u0304|\/N or \u2211|dx\u0304<\/sub>|\/N<\/span><\/span><\/strong><\/p>\n

\u092e\u093e\u0927\u094d\u092f \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0915\u093e \u0917\u0941\u0923\u093e\u0902\u0915 (CMD) = \u03b4x\u0304<\/sub>\/x\u0304<\/span><\/strong><\/span><\/p>\n

Co-efficient of Mean Deviation<\/span><\/strong><\/span><\/p>\n

✍️ \u03b4M<\/sub> = \u2211|x-M|\/N or \u2211|dM<\/sub>|\/N<\/span><\/strong><\/p>\n

\u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 (CMD) = \u03b4M<\/sub>\/M<\/span><\/strong><\/span><\/p>\n

Co-efficient of Mean Deviation<\/span><\/strong><\/span><\/p>\n

✍️\u00a0\u03b4Z<\/sub> = \u2211|x-z|\/N or \u2211|dz<\/sub>|\/N<\/span><\/strong><\/p>\n

\u092c\u0939\u0941\u0932\u0915 \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 (CMD) = \u00a0\u03b4Z<\/sub>\/Z<\/span><\/strong><\/span><\/p>\n

Co-efficient of Mean Deviation<\/span><\/strong><\/span><\/p>\n

NOTE: Mean deviation<\/strong><\/span><\/p>\n

✍️ With the help of Mean<\/strong><\/span><\/p>\n

✍️ With the help of Median \u092f\u0939\u0940 \u0926\u094b \u092a\u094d\u0930\u091a\u0932\u093f\u0924 \u0939\u0948\u0964\u00a0<\/strong><\/span><\/p>\n

✍️ \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e \u0938\u0947 \u0914\u0938\u0924 \u0935\u093f\u091a\u0932\u0928 \u0938\u092c\u0938\u0947 \u0909\u092a\u092f\u0941\u0915\u094d\u0924 \u092e\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u091a\u0930\u092e \u092e\u093e\u0928\u094b\u0902 \u0915\u093e \u092a\u094d\u0930\u092d\u093e\u0935 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/strong><\/span><\/p>\n

Example (i) \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0906\u0902\u0915\u0921\u093c\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f \u0914\u0930 \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e \u0915\u0940 \u0938\u0939\u093e\u092f\u0924\u093e \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902:<\/span><\/span><\/p>\n

Calculate mean deviation with the help of mean and median of the following data:<\/span><\/p>\n\n\n\n\n\n\n\n\n
S.No.<\/span><\/strong><\/span><\/td>\nX<\/strong><\/span><\/td>\n<\/tr>\n
1<\/strong><\/span><\/td>\n5<\/strong><\/span><\/td>\n<\/tr>\n
2<\/strong><\/span><\/td>\n8<\/strong><\/span><\/td>\n<\/tr>\n
3<\/strong><\/span><\/td>\n11<\/strong><\/span><\/td>\n<\/tr>\n
4<\/strong><\/span><\/td>\n12<\/strong><\/span><\/td>\n<\/tr>\n
5<\/strong><\/span><\/td>\n14<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u0939\u0932:<\/span><\/strong><\/span><\/p>\n

✍️ With the help of Mean<\/strong><\/span><\/p>\n\n\n\n\n\n\n\n\n\n
S.No.<\/span><\/strong><\/span><\/td>\nX<\/strong><\/span><\/td>\nx – x\u0304<\/strong><\/span><\/td>\n<\/tr>\n
1<\/strong><\/span><\/td>\n5<\/strong><\/span><\/td>\n5<\/strong><\/span><\/td>\n<\/tr>\n
2<\/strong><\/span><\/td>\n8<\/strong><\/span><\/td>\n2<\/strong><\/span><\/td>\n<\/tr>\n
3<\/strong><\/span><\/td>\n11<\/strong><\/span><\/td>\n1<\/strong><\/span><\/td>\n<\/tr>\n
4<\/strong><\/span><\/td>\n12<\/strong><\/span><\/td>\n2<\/strong><\/span><\/td>\n<\/tr>\n
5<\/strong><\/span><\/td>\n14<\/strong><\/span><\/td>\n4<\/strong><\/span><\/td>\n<\/tr>\n
\u00a0<\/strong><\/span><\/td>\nN = 50<\/strong><\/span><\/td>\n14<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

M.D. (\u03b4x\u0304) <\/sub>= \u2211|x-x\u0304|\/N or \u2211|dx\u0304<\/sub>|\/N<\/span><\/p>\n

NOTE: Modulus \u0915\u093e \u092e\u0924\u0932\u092c \u0915\u0947\u0935\u0932 positive \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/strong><\/span><\/p>\n

x\u0304 = \u03a3x\/N<\/strong><\/span><\/p>\n

\u00a0 \u00a0 = 50\/5<\/span><\/p>\n

\u00a0 \u00a0 = 10<\/span><\/p>\n

Now, \u03b4x\u0304 = \u2211|x-x\u0304|\/N<\/sub><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 14\/5<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 2.8\u00a0<\/span><\/p>\n

\u092e\u093e\u0927\u094d\u092f \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0915\u093e \u0917\u0941\u0923\u093e\u0902\u0915 (CMD) <\/span><\/p>\n

= \u03b4x\u0304<\/sub>\/x\u0304<\/span><\/p>\n

\u00a0= 2.8\/10<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 0.28<\/span><\/p>\n

✍️ With the help of Median<\/strong><\/span><\/p>\n

\u0928\u094b\u091f: \u092f\u0939\u093e\u0901 \u0938\u092c\u0938\u0947 \u092a\u0939\u0932\u0947 X \u0915\u0947 \u092e\u093e\u0928 \u0915\u094b \u092c\u095d\u0924\u0947 \u0915\u094d\u0930\u092e \u092e\u0947\u0902 Arrange \u0915\u0930\u0928\u093e \u0939\u0948 \u0939\u0932\u093e\u0902\u0915\u093f \u092f\u0939\u093e\u0901 \u092a\u0939\u0932\u0947 \u0938\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092e\u0947\u0902 \u0939\u0940 Arrange \u0939\u0948\u0964<\/strong><\/span><\/p>\n\n\n\n\n\n\n\n\n\n
S.No.<\/span><\/strong><\/span><\/td>\nX<\/strong><\/span><\/td>\nX-M<\/strong><\/span><\/td>\n<\/tr>\n
1<\/strong><\/span><\/td>\n5<\/strong><\/span><\/td>\n6<\/strong><\/span><\/td>\n<\/tr>\n
2<\/strong><\/span><\/td>\n8<\/strong><\/span><\/td>\n3<\/strong><\/span><\/td>\n<\/tr>\n
3<\/strong><\/span><\/td>\n11<\/strong><\/span><\/td>\n0<\/strong><\/span><\/td>\n<\/tr>\n
4<\/strong><\/span><\/td>\n12<\/strong><\/span><\/td>\n1<\/strong><\/span><\/td>\n<\/tr>\n
5<\/strong><\/span><\/td>\n14<\/strong><\/span><\/td>\n3<\/strong><\/span><\/td>\n<\/tr>\n
\u00a0<\/strong><\/span><\/td>\n<\/td>\nTotal sum = 13<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u03b4M<\/sub> = \u2211|x-M|\/N or \u2211|dM<\/sub>|\/N<\/span><\/p>\n

\u00a0Median = (n+1\/2)th <\/sup>Observation<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= (5+1\/2)th <\/sup>Observation<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 =( 6\/2)th <\/sup>Observation<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 3th <\/sup>Observation<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 11<\/span><\/p>\n

Now, MD (\u03b4M)<\/sub> = \u2211|x-M|\/N or \u2211|dM<\/sub>|\/N<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 13\/5<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 2.6<\/span><\/p>\n

\u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 (CMD) = \u03b4M<\/sub>\/M<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 2.6\/11<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 0.23<\/span><\/p>\n

\u0928\u094b\u091f: \u092f\u0939\u093e\u0901 \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0928\u093e \u0939\u0948 \u0915\u093f Mean \u0914\u0930 Median \u0905\u0932\u0917-\u0905\u0932\u0917 \u0939\u094b\u0924\u093e \u0939\u0948, \u0907\u0938\u0940\u0932\u093f\u090f MD \u092d\u0940 \u0905\u0932\u0917-\u0905\u0932\u0917 \u0939\u094b\u0917\u093e\u0964<\/strong><\/span><\/p>\n

(ii) \u0916\u0923\u094d\u0921\u093f\u0924 \u0936\u094d\u0930\u0947\u0923\u0940 (Discrete Series)<\/strong><\/span><\/p>\n

\u092a\u094d\u0930\u0924\u094d\u092f\u0915\u094d\u0937 \u0930\u0940\u0924\u093f (Direct Method)-<\/strong><\/span> \u0916\u0923\u094d\u0921\u093f\u0924 \u0936\u094d\u0930\u0947\u0923\u0940 \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u094d\u092f\u0915\u094d\u0937 \u0930\u0940\u0924\u093f \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0930\u0928\u0940 \u092a\u0921\u093c\u0924\u0940 \u0939\u0948:<\/span><\/p>\n

(i) \u091c\u093f\u0938 \u092e\u093e\u0927\u094d\u092f \u0938\u0947 \u0935\u093f\u091a\u0932\u0928 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u093e \u0939\u0948, \u0909\u0938\u0947 \u091c\u094d\u091e\u093e\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

(ii) \u0909\u0938 \u092e\u093e\u0927\u094d\u092f \u0938\u0947 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0906\u0915\u093e\u0930 (x\u0304<\/span>) \u0915\u0947 \u0928\u093f\u0930\u092a\u0947\u0915\u094d\u0937 \u0935\u093f\u091a\u0932\u0928 |dx\u0304<\/sub>|<\/span><\/strong>\u00a0\u091c\u094d\u091e\u093e\u0924 \u0915\u093f\u092f\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0964<\/span><\/p>\n

(iii) \u0928\u093f\u0930\u092a\u0947\u0915\u094d\u0937 \u0935\u093f\u091a\u0932\u0928\u094b\u0902 |dx\u0304<\/sub>|<\/span><\/strong> \u0915\u094b \u0938\u092e\u094d\u092c\u0928\u094d\u0927\u093f\u0924 \u0906\u0935\u0943\u0924\u094d\u0924\u093f\u092f\u094b\u0902 \u0938\u0947 \u0917\u0941\u0923\u093e \u0915\u0930\u0915\u0947, \u0917\u0941\u0923\u0928\u092b\u0932\u094b\u0902 \u0915\u093e \u092f\u094b\u0917: \u03a3f<\/span><\/strong>|dx\u0304<\/sub>|, \u03a3f|d<\/span><\/strong><\/span>M<\/sub><\/span><\/strong>|, \u03a3f|dz<\/sub>|,<\/span><\/strong> \u091c\u094d\u091e\u093e\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/span><\/p>\n

(iv) \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0942\u0924\u094d\u0930 \u0915\u0947 \u092a\u094d\u0930\u092f\u094b\u0917 \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u091c\u094d\u091e\u093e\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948: \u03b4x\u0304, <\/sub>= \u03a3f|dx\u0304<\/sub>|\/N ,<\/sub>\u03b4M <\/sub>= \u03a3f|dM<\/sub>|\/N,\u00a0<\/sub><\/span><\/strong><\/span> \u03b4Z<\/sub>= \u03a3f|dz<\/sub>|\/N<\/span><\/strong><\/span><\/p>\n

(v) \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0917\u0941\u0923\u093e\u0902\u0915 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u092e\u0947\u0902 \u0938\u092e\u094d\u092c\u0928\u094d\u0927\u093f\u0924 \u092e\u093e\u0927\u094d\u092f \u0915\u093e \u092d\u093e\u0917 \u0926\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

Example (ii) \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0906\u0902\u0915\u0921\u093c\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f \u0914\u0930 \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e \u0915\u0940 \u0938\u0939\u093e\u092f\u0924\u093e \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902:<\/span><\/span><\/p>\n

Calculate mean deviation with the help of mean and median of the following data:<\/span><\/p>\n\n\n\n\n\n\n\n
\u0906\u0915\u093e\u0930 (Size)<\/strong><\/span><\/td>\n\u0906\u0935\u0943\u0924\u093f (Frequency)<\/strong><\/span><\/td>\n<\/tr>\n
10<\/strong><\/span><\/td>\n3<\/strong><\/span><\/td>\n<\/tr>\n
11<\/strong><\/span><\/td>\n12<\/strong><\/span><\/td>\n<\/tr>\n
12<\/strong><\/span><\/td>\n18<\/strong><\/span><\/td>\n<\/tr>\n
13<\/strong><\/span><\/td>\n12<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u0939\u0932:<\/span><\/p>\n

✍️ <\/span>With the help of mean<\/strong><\/span><\/p>\n\n\n\n\n\n\n\n\n
x<\/strong><\/span><\/td>\nf<\/strong><\/span><\/td>\nfx<\/strong><\/span><\/td>\n\u0964<\/span>x – x\u0304\u0964<\/span><\/strong><\/span><\/td>\nf\u0964<\/span>x – x\u0304\u0964<\/span><\/span><\/strong><\/span><\/td>\n<\/tr>\n
10<\/span><\/td>\n3<\/span><\/td>\n30<\/span><\/td>\n1.87<\/span><\/td>\n5.16<\/span><\/td>\n<\/tr>\n
11<\/span><\/td>\n12<\/span><\/td>\n132<\/span><\/td>\n0.87<\/span><\/td>\n10.44<\/span><\/td>\n<\/tr>\n
12<\/span><\/td>\n18<\/span><\/td>\n216<\/span><\/td>\n0.13<\/span><\/td>\n2.39<\/span><\/td>\n<\/tr>\n
13<\/span><\/td>\n12<\/span><\/td>\n156<\/span><\/td>\n1.13<\/span><\/td>\n13.56<\/span><\/td>\n<\/tr>\n
Total<\/span><\/td>\n45<\/span><\/td>\n534<\/span><\/td>\n–<\/span><\/td>\n31.95<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

x\u0304 = \u03a3fx\/\u03a3f<\/span><\/strong><\/span><\/p>\n

= 534\/45<\/span><\/p>\n

= 11.87<\/span><\/p>\n

MD (\u03b4x\u0304), <\/sub>= \u03a3f|x – x\u0304<\/span>|\/\u03a3f or \u03a3f|dx\u0304<\/sub>|\/\u03a3f <\/span><\/strong><\/span><\/span><\/p>\n

= 31.95\/45<\/span><\/p>\n

= 0.71<\/span><\/p>\n

Co-efficient of MD = MD\/x\u0304<\/span><\/strong><\/span><\/p>\n

= 0.71\/11.87<\/span><\/p>\n

= 0.095<\/span><\/p>\n

✍️ With the help of Median<\/strong><\/span><\/p>\n\n\n\n\n\n\n\n\n
x<\/strong><\/span><\/td>\nf<\/strong><\/span><\/td>\nCf<\/strong><\/span><\/td>\n|X-M|<\/strong><\/span><\/td>\nf|X-M|<\/strong><\/span><\/td>\n<\/tr>\n
10<\/span><\/td>\n3<\/span><\/td>\n3 (0-3)<\/span><\/td>\n2<\/span><\/td>\n6<\/span><\/td>\n<\/tr>\n
11<\/span><\/td>\n12<\/span><\/td>\n15 (3-15)<\/span><\/td>\n1<\/span><\/td>\n12<\/span><\/td>\n<\/tr>\n
12<\/span><\/strong><\/span><\/td>\n18<\/span><\/strong><\/span><\/td>\n33 (15-33)<\/span><\/strong><\/span><\/td>\n0<\/span><\/strong><\/span><\/td>\n0<\/span><\/strong><\/span><\/td>\n<\/tr>\n
13<\/span><\/td>\n12<\/span><\/td>\n45 (33-45)<\/span><\/td>\n1<\/span><\/td>\n12<\/span><\/td>\n<\/tr>\n
Total<\/span><\/td>\n45<\/span><\/td>\n–<\/span><\/td>\n–<\/span><\/td>\n30<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u00a0here, M = (N+1\/2)th<\/sup> term<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = (45+1\/2)th term<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = (46\/2)th term <\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 23th term<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 12<\/span><\/p>\n

now, <\/span><\/p>\n

MD (\u03b4M) = \u03a3f|X-M|\/\u03a3f <\/span><\/strong><\/span> or \u03a3f|dM|\/\u03a3f <\/span><\/strong><\/span><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 30\/45<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 0.66<\/span><\/p>\n

Co-efficient of MD = MD\/\u03b4M<\/sub><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 0.66\/12<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 0.055<\/span><\/p>\n

(iii) \u0938\u0924\u0924\u094d \u0936\u094d\u0930\u0947\u0923\u0940 (Continuous Series)<\/strong><\/span><\/h3>\n

\u0905\u0935\u093f\u091a\u094d\u091b\u093f\u0928\u094d\u0928 \u0905\u0925\u0935\u093e \u0938\u0924\u0924\u094d \u0936\u094d\u0930\u0947\u0923\u0940 \u092e\u0947\u0902 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0915\u0940 \u0917\u0923\u0928\u093e <\/span><\/strong><\/span><\/p>\n

(Calculation of Mean Deviation in Continuous Series)- <\/span><\/strong><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0\u0905\u0935\u093f\u091a\u094d\u091b\u093f\u0928\u094d\u0928 \u0905\u0925\u0935\u093e \u0938\u0924\u0924\u094d \u0936\u094d\u0930\u0947\u0923\u0940 \u092e\u0947\u0902 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0935\u0939\u0940 \u0930\u0940\u0924\u093f \u0939\u0948 \u091c\u094b \u0916\u0923\u094d\u0921\u093f\u0924 \u0936\u094d\u0930\u0947\u0923\u0940 \u092e\u0947\u0902 \u0905\u092a\u0928\u093e\u092f\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0964 \u0915\u0947\u0935\u0932 \u0907\u0924\u0928\u093e \u0905\u0928\u094d\u0924\u0930 \u0939\u0948 \u0915\u093f \u0938\u0924\u0924\u094d \u0936\u094d\u0930\u0947\u0923\u0940 \u092e\u0947\u0902 \u092e\u0927\u094d\u092f-\u092c\u093f\u0928\u094d\u0926\u0941 (mid-point) ‘m’ \u0928\u093f\u0915\u093e\u0932\u0915\u0930 \u0909\u0928\u094d\u0939\u0947\u0902 \u092e\u0942\u0932\u094d\u092f \u092e\u093e\u0928 \u0932\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u0924\u0924\u094d \u0936\u094d\u0930\u0947\u0923\u0940 \u090f\u0915 \u0916\u0923\u094d\u0921\u093f\u0924 \u0936\u094d\u0930\u0947\u0923\u0940 \u0915\u093e \u0938\u094d\u0935\u0930\u0942\u092a \u0932\u0947 \u0932\u0947\u0924\u0940 \u0939\u0948\u0964 \u0905\u0928\u094d\u092f \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901 \u0935\u0948\u0938\u0940 \u0939\u0940 \u0930\u0939\u0924\u0940 \u0939\u0948\u0964<\/span><\/p>\n

Example (iii) \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0906\u0902\u0915\u0921\u093c\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f \u0914\u0930 \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e \u0915\u0940 \u0938\u0939\u093e\u092f\u0924\u093e \u0938\u0947 \u092e\u093e\u0927\u094d\u092f \u0935\u093f\u091a\u0932\u0928 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902:<\/span><\/p>\n

Calculate mean deviation with the help of mean and median of the following data:<\/span><\/p>\n\n\n\n\n\n\n\n
Class<\/strong><\/span><\/td>\n\u0906\u0935\u0943\u0924\u093f (Frequency)<\/strong><\/span><\/td>\n<\/tr>\n
2-4<\/strong><\/span><\/td>\n3<\/strong><\/span><\/td>\n<\/tr>\n
4-6<\/strong><\/span><\/td>\n4<\/strong><\/span><\/td>\n<\/tr>\n
6-8<\/strong><\/span><\/td>\n2<\/strong><\/span><\/td>\n<\/tr>\n
8-10<\/span><\/td>\n1<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u0939\u0932:<\/strong><\/span><\/p>\n

✍️ <\/span>With the help of mean<\/strong><\/span><\/p>\n\n\n\n\n\n\n\n\n
x<\/strong><\/span><\/td>\nf<\/strong><\/span><\/td>\nmv<\/strong><\/span><\/td>\nfmv<\/strong><\/span><\/td>\n\u0964<\/span>x – x\u0304\u0964<\/span><\/strong><\/span><\/td>\nf\u0964x – x\u0304\u0964<\/span><\/strong><\/span><\/td>\n<\/tr>\n
2-4<\/strong><\/span><\/td>\n3<\/strong><\/span><\/td>\n3<\/span><\/td>\n9<\/span><\/td>\n2.2<\/strong><\/span><\/td>\n6.6<\/strong><\/span><\/td>\n<\/tr>\n
4-6<\/strong><\/span><\/td>\n4<\/strong><\/span><\/td>\n5<\/span><\/td>\n20<\/span><\/td>\n0.2<\/strong><\/span><\/td>\n0.8<\/strong><\/span><\/td>\n<\/tr>\n
6-8<\/strong><\/span><\/td>\n2<\/strong><\/span><\/td>\n7<\/span><\/td>\n14<\/span><\/td>\n1.8<\/strong><\/span><\/td>\n3.6<\/strong><\/span><\/td>\n<\/tr>\n
8-10<\/span><\/td>\n1<\/strong><\/span><\/td>\n9<\/span><\/td>\n9<\/span><\/td>\n3.8<\/strong><\/span><\/td>\n3.8<\/strong><\/span><\/td>\n<\/tr>\n
Total<\/span><\/td>\n10<\/strong><\/span><\/td>\n–<\/span><\/td>\n52<\/span><\/td>\n–<\/strong><\/span><\/td>\n14.8<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Note: x = mv\u00a0<\/span><\/p>\n

MD (\u03b4x\u0304), <\/sub>= \u03a3f|x – x\u0304|\/\u03a3f or \u03a3f|dx\u0304<\/sub>|\/\u03a3f <\/span><\/strong><\/span><\/span><\/p>\n

here,\u00a0 x\u0304 = \u03a3fmv\/\u03a3f<\/span><\/strong><\/span><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 52\/10<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 5.2<\/span><\/p>\n

now, MD (\u03b4x\u0304), <\/sub>= \u03a3f|x – x\u0304|\/\u03a3f\u00a0<\/span><\/strong><\/span><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 14.8\/10<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 1.48<\/span><\/p>\n

Co-efficient of MD<\/a> = MD\/x\u0304<\/span><\/strong><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 1.48\/5.2<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 0.28<\/span><\/p>\n

✍️ With the help of Median<\/a><\/strong><\/span><\/p>\n\n\n\n\n\n\n\n\n
x<\/strong><\/span><\/td>\nf<\/strong><\/span><\/td>\ncf<\/td>\nmv<\/strong><\/span><\/td>\n\u0964X<\/span>– M\u0964<\/span><\/strong><\/span><\/td>\nf\u0964X- M\u0964<\/span><\/strong><\/span><\/td>\n<\/tr>\n
2-4<\/strong><\/span><\/td>\n3<\/strong><\/span><\/td>\n3<\/td>\n3<\/span><\/td>\n2<\/td>\n6<\/td>\n<\/tr>\n
4-6<\/strong><\/span><\/td>\n4<\/strong><\/span><\/td>\n7<\/span><\/td>\n5<\/span><\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n
6-8<\/strong><\/span><\/td>\n2<\/strong><\/span><\/td>\n9<\/td>\n7<\/span><\/td>\n2<\/td>\n4<\/td>\n<\/tr>\n
8-10<\/span><\/td>\n1<\/strong><\/span><\/td>\n10<\/td>\n9<\/span><\/td>\n4<\/td>\n4<\/td>\n<\/tr>\n
Total<\/span><\/td>\n10<\/strong><\/span><\/td>\n–<\/span><\/td>\n\u00a0<\/span><\/td>\n<\/td>\n14<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

MD (\u03b4M) = \u03a3f|X-M|\/\u03a3f<\/span><\/strong><\/span><\/span><\/p>\n

here, M (Median) = (N+1\/2)th<\/sup> term<\/p>\n

= (10+1\/2)th<\/sup> term<\/p>\n

= 5.5th<\/sup> term<\/p>\n

= (4-6) =4<\/strong><\/span><\/p>\n

\"\"<\/p>\n

L = 4<\/p>\n

N = \u03a3f = 10<\/p>\n

cf = 3<\/p>\n

f = 4<\/p>\n

h = 2<\/p>\n

now, M = 4+10\/2-3\/4 x 2<\/p>\n

= 4 +2\/2<\/p>\n

= 5<\/p>\n

MD (\u03b4M) = \u03a3f|X-M|\/\u03a3f<\/span><\/strong><\/span><\/span><\/p>\n

= 14\/10<\/p>\n

= 1.4<\/strong><\/span><\/p>\n

Co-efficient of MD<\/a> = MD\/M<\/span><\/strong><\/span><\/p>\n

= 1.5\/5<\/p>\n

\u00a0 \u00a0= 0.28<\/strong><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Mean Deviation (\u0914\u0938\u0924 \u0935\u093f\u091a\u0932\u0928) Definition \/ \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u00a0 \u00a0 \u00a0 Mean Deviation is a statistical measure of dispersion which is calculated as the average of absolute deviations of observations from a central value (Mean, Median or Mode). \u00a0 \u00a0 \u0914\u0938\u0924 \u0935\u093f\u091a\u0932\u0928 \u0935\u0939 \u092a\u094d\u0930\u0938\u093e\u0930 \u092e\u093e\u092a \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 \u0938\u092d\u0940 \u092a\u094d\u0930\u0947\u0915\u094d\u0937\u0923\u094b\u0902 \u0915\u0947 \u0915\u093f\u0938\u0940 \u0915\u0947\u0902\u0926\u094d\u0930\u0940\u092f \u092e\u093e\u0928 (\u092e\u093e\u0927\u094d\u092f, \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e \u092f\u093e […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[56,55,162],"tags":[],"class_list":["post-20417","post","type-post","status-publish","format-standard","hentry","category-ba-semester-paper-iv","category-ba-semester-paper-v","category-research-methodology"],"acf":{"test_duration":60,"q1_question":"","q1_option_a":"","q1_option_b":"","q1_option_c":"","q1_option_d":"","q1_correct":"","q1_explanation":"","q2_question":"","q2_option_a":"","q2_option_b":"","q2_option_c":"","q2_option_d":"","q2_correct":"","q2_explanation":"","q3_question":"","q3_option_a":"","q3_option_b":"","q3_option_c":"","q3_option_d":"","q3_correct":"","q3_explanation":"","q4_question":"","q4_option_a":"","q4_option_b":"","q4_option_c":"","q4_option_d":"","q4_correct":"","q4_explanation":"","q5_question":"","q5_option_a":"","q5_option_b":"","q5_option_c":"","q5_option_d":"","q5_correct":"","q5_explanation":"","q6_question":"","q6_option_a":"","q6_option_b":"","q6_option_c":"","q6_option_d":"","q6_correct":"","q6_explanation":"","q7_question":"","q7_option_a":"","q7_option_b":"","q7_option_c":"","q7_option_d":"","q7_correct":"","q7_explanation":"","q8_question":"","q8_option_a":"","q8_option_b":"","q8_option_c":"","q8_option_d":"","q8_correct":"","q8_explanation":"","q9_question":"","q9_option_a":"","q9_option_b":"","q9_option_c":"","q9_option_d":"","q9_correct":"","q9_explanation":"","q10_question":"","q10_option_a":"","q10_option_b":"","q10_option_c":"","q10_option_d":"","q10_correct":"","q10_explanation":"","q11_question":"","q11_option_a":"","q11_option_b":"","q11_option_c":"","q11_option_d":"","q11_correct":"","q11_explanation":"","q12_question":"","q12_option_a":"","q12_option_b":"","q12_option_c":"","q12_option_d":"","q12_correct":"","q12_explanation":"","q13_question":"","q13_option_a":"","q13_option_b":"","q13_option_c":"","q13_option_d":"","q13_correct":"","q13_explanation":"","q14_question":"","q14_option_a":"","q14_option_b":"","q14_option_c":"","q14_option_d":"","q14_correct":"","q14_explanation":"","q15_question":"","q15_option_a":"","q15_option_b":"","q15_option_c":"","q15_option_d":"","q15_correct":"","q15_explanation":"","q16_question":"","q16_option_a":"","q16_option_b":"","q16_option_c":"","q16_option_d":"","q16_correct":"","q16_explanation":"","q17_question":"","q17_option_a":"","q17_option_b":"","q17_option_c":"","q17_option_d":"","q17_correct":"","q17_explanation":"","q18_question":"","q18_option_a":"","q18_option_b":"","q18_option_c":"","q18_option_d":"","q18_correct":"","q18_explanation":"","q19_question":"","q19_option_a":"","q19_option_b":"","q19_option_c":"","q19_option_d":"","q19_correct":"","q19_explanation":"","q20_question":"","q20_option_a":"","q20_option_b":"","q20_option_c":"","q20_option_d":"","q20_correct":"","q20_explanation":"","q21_question":"","q21_option_a":"","q21_option_b":"","q21_option_c":"","q21_option_d":"","q21_correct":"","q21_explanation":"","q22_question":"","q22_option_a":"","q22_option_b":"","q22_option_c":"","q22_option_d":"","q22_correct":"","q22_explanation":"","q23_question":"","q23_option_a":"","q23_option_b":"","q23_option_c":"","q23_option_d":"","q23_correct":"","q23_explanation":"","q24_question":"","q24_option_a":"","q24_option_b":"","q24_option_c":"","q24_option_d":"","q24_correct":"","q24_explanation":"","q25_question":"","q25_option_a":"","q25_option_b":"","q25_option_c":"","q25_option_d":"","q25_correct":"","q25_explanation":"","q26_question":"","q26_option_a":"","q26_option_b":"","q26_option_c":"","q26_option_d":"","q26_correct":"","q26_explanation":"","q27_question":"","q27_option_a":"","q27_option_b":"","q27_option_c":"","q27_option_d":"","q27_correct":"","q27_explanation":"","q28_question":"","q28_option_a":"","q28_option_b":"","q28_option_c":"","q28_option_d":"","q28_correct":"","q28_explanation":"","q29_question":"","q29_option_a":"","q29_option_b":"","q29_option_c":"","q29_option_d":"","q29_correct":"","q29_explanation":"","q30_question":"","q30_option_a":"","q30_option_b":"","q30_option_c":"","q30_option_d":"","q30_correct":"","q30_explanation":"","q31_question":"","q31_option_a":"","q31_option_b":"","q31_option_c":"","q31_option_d":"","q31_correct":"","q31_explanation":"","q32_question":"","q32_option_a":"","q32_option_b":"","q32_option_c":"","q32_option_d":"","q32_correct":"","q32_explanation":"","q33_question":"","q33_option_a":"","q33_option_b":"","q33_option_c":"","q33_option_d":"","q33_correct":"","q33_explanation":"","q34_question":"","q34_option_a":"","q34_option_b":"","q34_option_c":"","q34_option_d":"","q34_correct":"","q34_explanation":"","q35_question":"","q35_option_a":"","q35_option_b":"","q35_option_c":"","q35_option_d":"","q35_correct":"","q35_explanation":"","q36_question":"","q36_option_a":"","q36_option_b":"","q36_option_c":"","q36_option_d":"","q36_correct":"","q36_explanation":"","q37_que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