Respuesta :
Answer:
If this is the sample data, the sample variance is 125.07 and the sample standard deviation is 11.18
If this is a population data, the population variance is 109.44 and the population standard deviation is 10.46
Step-by-step explanation:
We are given the following data-set:
70, 65, 71, 78, 89, 68, 50, 75
Deviations from the mean
–0.75, –5.75 , 0.25, 7.25, 18.25, –2.75, –20.75, 4.2
Sample size, n = 8
Sample:
[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.
Sum of squares of differences =
0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5
[tex]s = \sqrt{\dfrac{875.5}{7}} = 11.18[/tex]
[tex]\text{ Sample variance} = s^2 = 125.07[/tex]
Population:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
Sum of squares of differences =
0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5
[tex]\sigma = \sqrt{\dfrac{875.5}{8}} = 10.46[/tex]
[tex]\text{ Population variance} = \sigma^2 = 109.44[/tex]
