Question

the number of adult wild cats observed in national parks is recorded: 20, 16, 11, 14, 52, 21, 19, 14, 13, 17. the park with 52 is considered an outlier. how will the mean number of adult wild cats be affected if the outlier is removed from the data set? explain your reasoning. the mean will increase because the outlier pulls the mean downward. the mean will be the same because the outlier does not affect the mean. the data must be graphed to determine how the mean will be affected. the mean will decrease because the outlier pulls the mean upward.

Explanation:

Step1: Calculate mean with outlier

Data: 20, 16, 11, 14, 52, 21, 19, 14, 13, 17
Sum = \(20 + 16 + 11 + 14 + 52 + 21 + 19 + 14 + 13 + 17 = 197\)
Count = 10
Mean (with outlier) = \(\frac{197}{10} = 19.7\)

Step2: Calculate mean without outlier (remove 52)

New data: 20, 16, 11, 14, 21, 19, 14, 13, 17
New sum = \(197 - 52 = 145\)
New count = 9
Mean (without outlier) = \(\frac{145}{9} \approx 16.11\)

Step3: Compare means

Original mean: 19.7, New mean: ~16.11. The outlier (52) is larger than most values, so removing it decreases the mean.

Answer:

The mean will decrease because the outlier pulls the mean upward.