Question

Identify the outlier in the data set, and determine how the outlier affects the mean, median, and mode of the data.

95, 88, 72, 26, 69, 78, 97

GROUP OF ANSWER CHOICES

A. 97; adding the outlier decreased mean by 5 and median by 8.2. The mode did not change.
B. 26; adding the outlier decreased mean by 8.2 and median by 5. The mode did not change.
C. 97; adding the outlier increased mean by 8.2 and median by 5. The mode did not change.
D. 26; adding the outlier increased mean by 5 and median by 8.2. The mode did not change.

Answer 1

B

Explanation:

26 is the smallest number in this data set by a lot. As for how it changes the three Ms:

Mean

Mean without outlier: 83.2

Mean with outlier: 75

83.2 - 75 = 8.2

Median: The middlemost number in the graph. Before the outlier was added, the median would be 83, since it is the average of the two middle most numbers; 78 and 88. With the addition of 26 to this data set, the median is now just 78. This overall leads to a decrease of 5.

83 - 78 = 5

Mode: The number that shows up the most. However, since all of these numbers show up only once, we can ignore this.

Therefore, the answer is B.