Q18. - Algebra 1

Question

Find the mean, variance, and standard deviation to the nearest tenth for the set of data.

15, 16, 16, 15, 16, 17, 18

Step-by-Step Solution

Answer

The mean is about 10.8, the variance is 1 and the standard deviation is 1.

Step 1. Define mean.

The mean is equal to the sum of all data values divided by the number of data values.

Step 2. Define the standard deviation.

The standard deviation is a calculated value that shows how the data deviates from the mean of the data.

Step 3. Define the variance.

The variance of the data is the square of the standard deviation. 

Step 4. Calculate the mean, variance, and standard deviation for the given set of data.

The set of data are:

15, 16, 16, 15, 16, 17, 18

Calculate the mean of the data.

Mean $$\begin{gathered} =\frac{15+16+16+15+16+17+18}{7} \\ =\frac{113}{7} \\ \approx 16.1 \end{gathered}$$

To find the variance, subtract the mean from each data and then square it and add and then divide by the numbers of data.

The variance is

$$\begin{gathered} =\frac{{\left(15-16.1\right)}^2+{\left(16-16.1\right)}^2+{\left(16-16.1\right)}^2+{\left(15-16.1\right)}^2+{\left(16-16.1\right)}^2+{\left(17-16.1\right)}^2+{\left(18-16.1\right)}^2}{7} \\ =\frac{6.87}{7} \\ \approx 1 \end{gathered}$$

To find the standard deviation, square root the variance.

The standard deviation is 

$$\begin{gathered} =\sqrt{1} \\ =1 \end{gathered}$$

 

Therefore, the mean is 10.8, the variance is 1 and the standard deviation is 1.