diego is a wildlife researcher. they were analyzing the mean and median lengths of 9 whales their team had…

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.

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.

Answer

Explanation:

Step1: Recall mean formula

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

Step2: Recall median concept

There are $n = 9$ (an odd - numbered) data points. The median is the 5th - ordered value when the data is arranged in ascending order. Changing the shortest value (the 1st - ordered value) 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.