Q.A data set of monthly incomes (in thousands of rupees) for seven households is: 10, 12, 15, 18, 20, 22, 25. Compute the arithmetic mean and the median of this data. If an eighth household with a very high income of Rs. 200 thousand is added, which of the two measures — mean or median — would be affected more, and why?

Apply the mean formula (sum ÷ N) and locate the middle value for the median, then reason about which measure an extreme addition would distort more.

Arithmetic Mean:

Median: the data is already arranged in ascending order: 10, 12, 15, 18, 20, 22, 25. With $N=7$ (an ODD number), the median is the single middle value — the 4th value in the ordered list, which is 18.

Effect of adding an extreme value: suppose an eighth household with income Rs. 200 thousand is added. The new mean becomes:

a jump of nearly Rs. 23 thousand from the original mean of 17.43 — a huge distortion caused by just ONE unusually high value, because the mean's formula directly SUMS every value's magnitude, including this outlier.

The new median, however, is found from the now EIGHT ordered values: 10, 12, 15, 18, 20, 22, 25, 200 — with an EVEN number of observations, the median is the average of the two middle (4th and 5th) values: $(18+20)/2=19$ — barely different from the original median of 18. The median moved only slightly because it depends purely on POSITION in the ordered list, not on how extreme the actual value at either end happens to be — the outlier of 200 could just as easily have been 2,000, and the median would move by exactly the same tiny amount. …

A common slip when computing the median of an EVEN-numbered data set is to pick just ONE of the two middle values instead of averaging both of them — with 8 observations, the …