Question

The data set shown below has an outlier. Determine the outlier and then answer the questions as to what happens to the median, mean, and mode when the outlier is removed.
Data: 29, 19, 35, 27, 21, 48, 23, 12, 24, 26, 20, 28, 30, 22, 19, 32, 22

Answer 1

The mean is the average value of the given data set. When the outlier is removed the mean and the median of the data set are changed.

What are mean, median, and mode?

• The mean is the average value of the given data set.
• The median is the middle value of a given data set when the data is arranged in increasing order.
• The mode is the number that is repeated the most number of times in a given data set.

The data set can be arranged as 12, 19, 19, 20, 21, 22, 22, 23, 24, 26, 27, 28, 29, 30, 32, 35, 48. Now, The means, median and mode for the data set is,

Mean = (29+19+35+27+21+48+23+12+24+26+20+28+30+22+19+32+22) / 17

Mean = 25.7

Median(The middle value when the data is arranged in increasing order) = 24

Mode = 19,22

The outlier in the data set is 48, therefore, the mean median and mode now will be,

12, 19, 19, 20, 21, 22, 22, 23, 24, 26, 27, 28, 29, 30, 32, 35

Mean = 24.3125

Median = 23.5

Mode = 19, 22

Hence, when the outlier is removed the mean and the median of the data set are changed.

Learn more about Mean, Median, and Mode:

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