[amp_mcq option1=”Mean” option2=”Mode” option3=”Median” option4=”Range” correct=”option3″]<\/p>\n
The correct answer is (c), median.<\/p>\n
Mean deviation is a measure of how spread out numbers are in a data set. It is calculated by taking the average of the absolute values of the differences between each number in the data set and the mean of the data set.<\/p>\n
The mean deviation is minimum with respect to the median because the median is the middle value in a data set. The absolute values of the differences between each number in the data set and the median are always less than or equal to the absolute values of the differences between each number in the data set and the mean.<\/p>\n
For example, consider the data set {1, 2, 3, 4, 5}. The mean of this data set is 3. The absolute values of the differences between each number in the data set and the mean are 2, 1, 0, 1, and 2. The mean deviation is $\\frac{2+1+0+1+2}{5}=\\frac{6}{5}$.<\/p>\n
The median of this data set is 3. The absolute values of the differences between each number in the data set and the median are 0, 1, 0, 1, and 0. The mean deviation is $\\frac{0+1+0+1+0}{5}=\\frac{2}{5}$.<\/p>\n
As you can see, the mean deviation is less when calculated with respect to the median than when calculated with respect to the mean. This is because the median is a more central value than the mean.<\/p>\n","protected":false},"excerpt":{"rendered":"
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