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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.

1 answer

To analyze how the mean is affected by an outlier, let's calculate the mean for both data sets:

  1. Data without an outlier: 15, 19, 22, 26, 29

    • Mean = (15 + 19 + 22 + 26 + 29) / 5
    • Mean = 111 / 5
    • Mean = 22.2

  2. Data with an outlier: 15, 19, 22, 26, 29, 81

    • Mean = (15 + 19 + 22 + 26 + 29 + 81) / 6
    • Mean = 192 / 6
    • Mean = 32

Now let's compare the means:

  • The mean without the outlier is 22.2.
  • The mean with the outlier is 32.

The outlier (81) increased the mean significantly.

Thus, the correct answer is: The outlier made the mean higher than all the other values.