Q:

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

Accepted Solution

A:
Answer: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.Step-by-step 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, 102Formula:[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{467}{11} = 42.4545[/tex]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[tex]S.D = \sqrt{\frac{16682.72727}{10}} = 40.8445[/tex]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.