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17. Measures of Dispersion

Learn how to easily memorize the standard deviation formula for grouped and ungrouped data. Follow simple steps and formulas to understand measures of dispersion better.

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17. Measures of Dispersion

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  1. (x1－x)2+(x2－x)2+…+(xn－x)2 σ= n x1+x2+…+xn x= n is the mean of the n data. 17. Measures of Dispersion How to memorise the formula of the standard deviation of grouped data? (i) Memorise the formula of the standard deviation of ungrouped data first. The standard deviation of ungrouped data is: where

  2. x= 17. Measures of Dispersion How to memorise the formula of the standard deviation of grouped data? (ii) Regard the grouped data as having f1‘x1’, f2‘x2’, … , fn‘xn’. Then, find the mean of the group of data. Regard the grouped data as having f1‘x1’, f2‘x2’, … , fn‘xn’. f1‘x1’, f2‘x2’, … , fn‘xn’ The number of data of the grouped data is N = f1+f2+…+fn N = f1+f2+…+fn The mean of the group of data is: f1x1+f2x2+…+fnxn f1+f2+…+fn N

  3. (x1－x)2+(x1－x)2+…+(x2－x)2+(x2－x)2+…+(xn－x)2 = N (x1－x)2+(x1－x)2+… = f1(x1－x)2 +(x1－x)2 17. Measures of Dispersion How to memorise the formula of the standard deviation of grouped data? (iii) Substitute f1‘x1’, f2‘x2’, … , fn‘xn’ into the formula of the standard deviation of ungrouped data. where a total of f1

  4. (x1－x)2+(x1－x)2+…+(x2－x)2+(x2－x)2+…+(xn－x)2 (x2－x)2+(x2－x)2+… = N = f2(x2－x)2 +(x2－x)2 17. Measures of Dispersion How to memorise the formula of the standard deviation of grouped data? (iii) Substitute f1‘x1’, f2‘x2’, … , fn‘xn’ into the formula of the standard deviation of ungrouped data. where a total of f2

  5. +(xn－x)2 = fn(xn－x)2 (xn－x)2+(xn－x)2+… 17. Measures of Dispersion How to memorise the formula of the standard deviation of grouped data? (iii) Substitute f1‘x1’, f2‘x2’, … , fn‘xn’ into the formula of the standard deviation of ungrouped data. (x1－x)2+(x1－x)2+…+(x2－x)2+(x2－x)2+…+(xn－x)2 = N where a total of fn

  6. (x1－x)2+(x1－x)2+…+(x2－x)2+(x2－x)2+…+(xn－x)2 …+(xn－x)2 (x2－x)2+(x2－x)2+… = N (x1－x)2+(x1－x)2+… …+fn(xn－x)2 f1(x1－x)2+ = f2(x2－x)2+ 17. Measures of Dispersion How to memorise the formula of the standard deviation of grouped data? (iii) Substitute f1‘x1’, f2‘x2’, … , fn‘xn’ into the formula of the standard deviation of ungrouped data. N f1+f2+…+fn

  7. 17. Measures of Dispersion How to memorise the formula of the standard deviation of grouped data? (i) Memorise the formula of the standard deviation of ungrouped data first. (ii) Regard the grouped data as having f1‘x1’, f2‘x2’, … , fn‘xn’. Then, find the mean of the group of data. (iii) Substitute f1‘x1’, f2‘x2’, … , fn‘xn’ into the formula of the standard deviation of ungrouped data.

  8. x1+x2+…+xn n f1x1+f2x2+…+fnxn f1+f2+…+fn 17. Measures of Dispersion Formula of standard deviation Easy Memory Tips:

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