Question

select the outlier in the data set.
49 47 39 55 56 99 67 43 45 53
29
if the outlier were removed from the data set, would the mean increase or decrease?
increase decrease

Explanation:

Step1: Identify the outlier

The data set is [29, 39, 43, 45, 47, 49, 53, 55, 56, 67, 99]. 99 is much larger than other values, so it is the outlier.

Step2: Calculate mean with outlier

Sum = 29 + 39 + 43 + 45 + 47 + 49 + 53 + 55 + 56 + 67 + 99 = 582
Mean = $\frac{582}{11} \approx 52.91$

Step3: Calculate mean without outlier

New sum = 582 - 99 = 483
New mean = $\frac{483}{10} = 48.3$

Step4: Compare means

48.3 < 52.91, so mean decreases.

Answer:

Outlier: 99
Mean change: decrease