Question

deepali was given two data sets, one without an outlier and one with an outlier.
data without an outlier: 15, 19, 22, 26, 29
data with an outlier: 15, 19, 22, 26, 29, 81
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 of data: \(15 + 19 + 22 + 26 + 29 = 111\)
Number of data points: \(5\)
Mean: \(\frac{111}{5} = 22.2\)

Step2: Calculate mean with outlier

Sum of data: \(15 + 19 + 22 + 26 + 29 + 81 = 192\)
Number of data points: \(6\)
Mean: \(\frac{192}{6} = 32\)

Step3: Analyze the effect

The outlier (81) is much larger than the other values. The mean with outlier (32) is higher than the mean without outlier (22.2) and higher than all the original data values (15, 19, 22, 26, 29).

Answer:

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