Respuesta :
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, 102
Formula:
[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.
