the numbers of regular season wins for 10 football teams in a given season are given below. determine the…

Explanation:

Step1: Find the range

Range = Max - Min. The maximum value in the data - set {2, 9, 15, 4, 13, 7, 15, 6, 2, 10} is 15 and the minimum value is 2. Range = 15 - 2

Step2: Find the mean

The mean $\mu$ of a population data - set $x_1,x_2,\cdots,x_n$ is $\mu=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here, $n = 10$, and $\sum_{i=1}^{10}x_i=2 + 9+15 + 4+13+7+15+6+2+10=83$. So, $\mu=\frac{83}{10}=8.3$.

Step3: Find the variance

The variance $\sigma^{2}$ of a population data - set is $\sigma^{2}=\frac{\sum_{i = 1}^{n}(x_i-\mu)^2}{n}$. $(2 - 8.3)^2=(-6.3)^2 = 39.69$, $(9 - 8.3)^2=(0.7)^2 = 0.49$, $(15 - 8.3)^2=(6.7)^2 = 44.89$, $(4 - 8.3)^2=(-4.3)^2 = 18.49$, $(13 - 8.3)^2=(4.7)^2 = 22.09$, $(7 - 8.3)^2=(-1.3)^2 = 1.69$, $(15 - 8.3)^2=(6.7)^2 = 44.89$, $(6 - 8.3)^2=(-2.3)^2 = 5.29$, $(2 - 8.3)^2=(-6.3)^2 = 39.69$, $(10 - 8.3)^2=(1.7)^2 = 2.89$. $\sum_{i = 1}^{10}(x_i - 8.3)^2=39.69+0.49+44.89+18.49+22.09+1.69+44.89+5.29+39.69+2.89 = 229.2$. $\sigma^{2}=\frac{229.2}{10}=22.92$.

Step4: Find the standard deviation

The standard deviation $\sigma$ of a population data - set is $\sigma=\sqrt{\sigma^{2}}$. So, $\sigma=\sqrt{22.92}\approx4.79$.

Answer:

Range: 13 Mean: 8.3 Variance: 22.92 Standard deviation: approximately 4.79