Question

sora was given two data sets, one without an outlier and one with an outlier.
data without an outlier: 108, 113, 105, 118, 124, 121, 109
data with an outlier: 108, 113, 105, 118, 124, 121, 109, 41
how is the mean affected by an outlier?
○ the outlier did not affect the mean at all.
○ the outlier made the mean higher than all the other values.
○ the outlier made the mean lower than all the other values.
○ the mean is centered around all the other numbers in both sets of data.

Explanation:

Step1: Calculate mean without outlier

Sum the data: \(108 + 113 + 105 + 118 + 124 + 121 + 109 = 798\)
Number of values: \(7\)
Mean: \(\frac{798}{7} = 114\)

Step2: Calculate mean with outlier

Sum the data (add 41): \(798 + 41 = 839\)
Number of values: \(8\)
Mean: \(\frac{839}{8} = 104.875\)

Step3: Compare means

The original mean (114) is higher than the other values (all data points except 41 are above 105). The new mean (104.875) is lower than all the other values (since 41 is much lower, pulling the mean down below the other data points).

Answer:

The outlier made the mean lower than all the other values.