Question

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.

Answer 1

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:

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

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

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{2971}{15} = 198.06$

The mean of sample is 198.06 pounds.

Sum of squares of differences = 7984.93

$S.D = \sqrt{\dfrac{7984.93}{14}} = 23.88$

The sample standard deviation is 23.88 pounds.

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

$x < \bar{x}- 2s\\x < 198.06 -2(23.88)\\x < 150.3$

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