The following are weights in pounds of a college sports team: 165, 171, 174, 180, 182, 188, 189, 192, 198, 202, 202, 225, 228, 235, 240.

Find the weight that is 2 standard deviations below the mean. Round your answer to the nearest pound.

Question

College

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Answer :

ChiKesselman ChiKesselman · Answer 1 · 2025-03-05T14:56:36-05:00

Answer:

There are no values in the data that is two standard deviations below the mean.

Step-by-step explanation:

We are given the following data set in question:

165, 171, 174, 180, 182, 188, 189, 192, 198, 202, 202, 225, 228, 235, 240

Formula:

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{2971}{15} = 198.06[/tex]

The mean of sample is 198.06 pounds.

Sum of squares of differences = 7984.93

[tex]S.D = \sqrt{\dfrac{7984.93}{14}} = 23.88[/tex]

The sample standard deviation is 23.88 pounds.

We have to find the weight that is 2 standard deviations below the mean.

[tex]x < \bar{x}- 2s\\x < 198.06 -2(23.88)\\x < 150.3[/tex]

Thus, we have to find a value less than 150.3.

Sorted data: 165, 171, 174, 180, 182, 188, 189, 192, 198, 202, 202, 225, 228, 235, 240

There are no values in the data that is less than 150.3