Question

liam works at a zoo. he was looking at some data showing the masses of their 5 african elephants. the mean mass of the elephants was 3,800 kg, and the median mass was 3,600 kg. the smallest elephant, named lola, weighed 2,700 kg. lola then got very sick and lost weight until her mass reached 1,800 kg. how will lolas mass decreasing affect the mean and median? choose 1 answer: a both the mean and median will decrease. b the mean will stay the same, and the median will decrease. c the mean will decrease, and the median will stay the same. d the mean will decrease, and the median will increase.

Explanation:

Step1: Recall mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here $n = 5$. When Lola's mass decreases, the sum $\sum_{i=1}^{n}x_{i}$ decreases while $n$ remains the same. So, the mean will decrease as $\bar{x}$ is directly related to the sum of the data - values.

Step2: Recall median concept

The median is the middle - value when the data is arranged in ascending or descending order. Since Lola is the smallest - valued data point, and there are 5 data points (an odd number), the median is the third - ordered value. Decreasing the smallest value does not change the third - ordered value. So, the median will stay the same.

Answer:

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