Question

diego is a wildlife researcher. they were analyzing the mean and median lengths of 9 whales their team had observed. the whales all had different lengths between 23 m and 27 m. diego found out that they were misreading the shortest length. it was actually 20 m, not 23 m. how will this length decreasing affect the mean and median? choose 1 answer: a both the mean and median will decrease. b the mean will decrease, and the median will increase. c the mean will decrease, and the median will stay the same. d the mean will stay the same, and the median will decrease.

Explanation:

Step1: Recall mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here $n = 9$. When the shortest - length value decreases from $23$m to $20$m, the sum $\sum_{i = 1}^{n}x_{i}$ decreases. Since $n$ is constant, the mean $\bar{x}$ will decrease.

Step2: Recall median concept

There are $n=9$ (an odd number) data - points. The median is the 5th - ordered value when the data is arranged in ascending order. Changing only the shortest value (the 1st - ordered value when arranged in ascending order) does not affect the 5th - ordered value. So the median stays the same.

Answer:

C. The mean will decrease, and the median will stay the same.