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  • Assertion: Mean deviation is a measure of dispersion that indicates the average distance between each data point and the mean of the data set.  Reason: Mean devia

Assertion: Mean deviation is a measure of dispersion that indicates the average distance between each data point and the mean of the data set. 

Reason: Mean deviation is computed by taking the absolute value of the difference between each data point and the mean, summing these absolute differences, and dividing by the number of data points. 

how does mean deviation differ from other measures of dispersion like variance and standard deviation?

 

Option: 1

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Option: 4

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Answers (1)

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Mean deviation differs from other measures of dispersion like variance and standard deviation in a few ways. First, unlike variance and standard deviation, mean deviation does not square the differences between each data point and the mean. This means that mean deviation is not affected by outliers in the data set as much as variance and standard deviation are. Second, because mean deviation uses absolute values, it does not differentiate between deviations above and below the mean. This can be an advantage in some cases where both positive and negative deviations are equally important. Finally, the mean deviation is less commonly used than a variance and standard deviation because it is less mathematically tractable and does not have the same desirable properties as those measures. For example, variance has the property that it is additive, which means that the variance of a sum of random variables is equal to the sum of the variances of those variables. Mean deviation does not have this property.

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