Question

Find the range, the standard deviation, and the variance for the given samples. Round non-integer results to the nearest tenth.8, 9, 13, 15, 16, 23, 25range-standard deviation-variance-

Answer 1

The range of a data is the interval that exists between the least and the greatest value:

`R=25-8=17`

The range is 17.

The standard deviation can be found using the following formula:

`\sigma=\sqrt{\frac{\Sigma(xi-\bar{x})^2}{n-1}}`

Where xi is any value of the samples, x^- is the mean of the sample and n is the number of samples:

`\bar{x}=(8+9+13+15+16+23+25)/(7)=15.57`
`\Sigma(xi-\bar{x})^2=(8-15.57)^2+(9-15.57)^2+(13-15.57)^2+(15-15.57)^2+(16-15.57)^2+(23-15.57)^2+(25-15.57)^2=251.71`
`\sigma=\sqrt{(251.71)/(7-1)}=6.5`

The standard deviation is 6.5.

The variance is found by finding the square of the standard deviation:

`\sigma^2=42.2`

The variance is 42.2.