Question

The lengths (in inches) of a sample of snakes in the Clarmont Zoo's reptile house are as follows: 9, 15, 86, 13, 16, 101, 85, 10, 14, 16, and 102. Describe in context what the standard deviation tells you about the data set

Answer 1

A higher value of standard deviation tells us that there is high variability in the length of the snake from the mean length of the snake.

Explanation:

We are given the following information in the question:

Sample of snakes in the Clarmont Zoo's reptile house are as follows:

9, 15, 86, 13, 16, 101, 85, 10, 14, 16, 102

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(467)/(11) = 42.4545`

Sum of squares of differences = 1119.206611 + 753.7520659 + 1896.206612 + 867.5702477 + 699.842975 + 3427.570248 + 1810.115703 + 1053.29752 + 809.6611568 + 699.842975 + 3545.661158 = 16682.72727

`S.D = \sqrt{(16682.72727)/(10)} = 40.8445`

Standard deviation:

• Standard deviation tells you how spread out the data is.
• It is a measure of how far each observed value is from the mean.
• A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.

A higher value of standard deviation tells us that there is high variability in the length of the snake from the mean length of the snake. The data is overspread over a wide range.