Find the mean deviation about the median for the following data: 4, 6, 9, 3, 10, 13, 2.

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4, 6, 9, 3, 10, 13, 2

Andhra Pradesh BieapBIEAP Intermediate Board 2023Subjective· 2mImportance★★★★★

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Sort the data, find the median, then average the absolute deviations of each value from the median.

Data: $4,6,9,3,10,13,2$ ( $n=7$ values). Sorted: $2,3,4,6,9,10,13$ .

Since $n=7$ is odd, the median is the $\left(\dfrac{n+1}{2}\right)=4$ th value in the sorted list: $\text{Median}=6$ .

Now find $|x_i-\text{Median}|$ for every value:

$|2-6|=4,\ |3-6|=3,\ |4-6|=2,\ |6-6|=0,\ |9-6|=3,\ |10-6|=4,\ |13-6|=7.$

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Q.Find the mean deviation about the median for the following data: $4, 6, 9, 3, 10, 13, 2$ .