The mean age of the students in this class is 15.75. The standard deviation is 1.55. Determine the number of standard deviations from the mean required to include of the ages listed.
13, 17, 18, 15, 16, 14, 15, 18, 17, 16, 15, 16, 13, 15, 17, 17

1.774 standard deviations

Step-by-step explanation:

From the data, the minimum value is x = 13 and the maximum value is x' = 18. The mean X = 15.75 and the standard deviation, σ = 1.55.

The difference between the mean and the minimum value is the deviation from the mean. So, X - x = 15.75 - 13 = 2.75. To find the number of standard deviations this is, we divide it by the standard deviation, σ = 1.55.

So, 2.75/1.55 = 1.774.

So, the number of standard deviations to contain the value 13 is 1.774σ

Also, the difference between the maximum value and the mean is the deviation from the mean. So, x' - X = 18 - 15.75 = 2.25. To find the number of standard deviations this is, we divide it by the standard deviation, σ = 1.55.

So, 2.25/1.55 = 1.452.

So, the number of standard deviations to contain the value 18 is 1.452σ

Since 1.774σ > 1.452σ and 1.774σ would contain both the values of 13 and 18, the number of standard deviations from the mean required to contain the values is  1.774 standard deviations.

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