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-BARSIC- [3]
3 years ago
7

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to o

ne more decimal place than the largest number of decimal places given in the data. 2,3,4,5,6,7,8,9,10,11
Mathematics
1 answer:
Zarrin [17]3 years ago
5 0

Answer:

The range of the data is 9.0.

The population variance is 8.25.

The population standard deviation is 2.87.

Step-by-step explanation:

The data set is: S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

(A)

The range of a data set is the difference between the maximum and minimum value of the data set.

Compute range as follows:

Range=Max.-Min.=11-2=9

Thus, the range of the data is 9.0.

(B)

The formula to compute the population variance is:

Var=\frac{1}{n} \sum (x_{i}-\bar x)^{2}

Compute the mean of the data set:

\bar x=\frac{1}{n} \sum x_{i}\\=\frac{1}{10}(2+3+4+5+6+7+8+9+10+11)\\=6.5

Compute the variance as follows:

Var=\frac{1}{n} \sum (x_{i}-\bar x)^{2}\\=\frac{1}{10}[(2-6.5)^{2}+(3-6.5)^{2} +(4-6.5)^{2}+...(11-6.5)^{2}]\\=8.25

Thus, the population variance is 8.25.

(C)

The population standard deviation is:

SD=\sqrt{Var} = \sqrt{\frac{1}{n} \sum (x_{i}-\bar x)^{2}}

Compute the population standard deviation of the data set:

SD=\sqrt{Var} = \sqrt{8.25}=2.87

Thus, the population standard deviation is 2.87.

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