Question

The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set2.7.15, 3, 12, 9, 15, 8, 3, 10 The range is 13(Simplify your answer.)The population mean is 8.4(Simplify your answer. Round to the nearest tenth as needed.)The population variance is(Simplify your answer. Round to the nearest tenth as needed.)The population standard deviation is (Simplify your answer. Round to the nearest tenth as needed)

Answer 1

We have the following data set:

2,7,15,3,12,9,15,8,3,10

The range is the difference between the highest and lowest values in the set, to find the range, order the data set from least to greatest.

2,3,3,7,8,9,10,12,15,15

Then,

$\begin{gathered} \text{Range}=15-2 \\ \text{Range}=13 \end{gathered}$

Mean is represented by the following expression:

$\text{Mean}=\frac{\text{Sum of all data points}}{Number\text{ of data po}ints}$$\text{Mean}=\frac{84}{10}=8.4$

Population variance formula looks like this:

$\begin{gathered} \sigma^2=\frac{\sum^{}_{}(x-\mu)^2}{N} \\ \text{where,} \\ \sigma^2=\text{population variance} \\ \sum ^{}_{}=addition\text{ of} \\ x=\text{each value} \\ \mu=population\text{ mean} \\ N=\text{ number of values in the population} \end{gathered}$

Then, substituting:

$\begin{gathered} \sigma^2=\frac{(2-14)^2+(3-14)^2+\cdots+(15-14)^2}{10} \\ \sigma^2=20.44 \end{gathered}$

For the standard deviation:

$\begin{gathered} s=\sqrt[]{\frac{\sum ^{}_{}(x-\mu)^2}{N}} \\ s=4.521 \end{gathered}$