Question

brandon works at a petting zoo with 8 animals. they were looking at some data showing the masses of the animals. each animal had a different mass between 2 and 160 kg. the zoo then buys a horse that weighs 900 kg as their 9th animal. how does buying the horse affect the mean and median? choose 1 answer: a both the mean and median will increase, but the median will increase by more than the mean. b both the mean and median will increase, but the mean will increase by more than the median. c both the mean and median will decrease, but the median will decrease by more than the mean. d both the mean and median will decrease, but the mean will decrease by more than the median.

Explanation:

Step1: Recall mean and median concepts

Mean is the sum of all values divided by number of values. Median is the middle - value when data is ordered.

Step2: Analyze the effect on the mean

The original 8 - animal data has values between 2 and 160 kg. The new value (900 kg) is much larger than the original values. The sum of the values will increase significantly, and since the number of values increases by 1, the mean will increase. Mathematically, if the sum of the original 8 values is $S_8$, the original mean $\bar{x}_8=\frac{S_8}{8}$. The new sum is $S_9 = S_8+900$, and the new mean $\bar{x}_9=\frac{S_8 + 900}{9}$. Since 900 is large, $\bar{x}_9>\bar{x}_8$.

Step3: Analyze the effect on the median

For 8 data points, the median is the average of the 4th and 5th ordered values. For 9 data points, the median is the 5th ordered value. Since the new value (900 kg) is larger than all the original values, when we order the 9 - value data set, the position of the median value shifts, but not as drastically as the mean. The median will increase, but not as much as the mean because the mean is influenced by the magnitude of the new large value.

Answer:

B. Both the mean and median will increase, but the mean will increase by more than the median.