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tiny-mole [99]
3 years ago
14

Consider a data set containing the following values: 70 65 71 78 89 68 50 75 The mean of the preceding values is 70.75. The devi

ations from the mean have been calculated as follows: –0.75 –5.75 0.25 7.25 18.25 –2.75 –20.75 4.2
If this is the sample data, the sample variance is _____ and the sample standard deviation is ___

If this is a population data, the population variance is_____ and the population standard deviation is_____
Mathematics
1 answer:
Leokris [45]3 years ago
7 0

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:

\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.

Sum of squares of differences =

0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5

s = \sqrt{\dfrac{875.5}{7}} = 11.18

\text{ Sample variance} = s^2 = 125.07

Population:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}  

where x_i are data points, \bar{x} 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

\sigma = \sqrt{\dfrac{875.5}{8}} = 10.46

\text{ Population variance} = \sigma^2 = 109.44

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