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

Explanation:

Step1: Arrange data in ascending order

$2,4,5,6,8,9,11,14,15,15$

Step2: Calculate the range

Range = Max - Min = $15 - 2=13$

Step3: Calculate the mean

$\bar{x}=\frac{2 + 4+5+6+8+9+11+14+15+15}{10}=\frac{89}{10}=8.9$

Step4: Calculate the variance

$\sigma^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n}$ $(2 - 8.9)^{2}=(-6.9)^{2}=47.61$ $(4 - 8.9)^{2}=(-4.9)^{2}=24.01$ $(5 - 8.9)^{2}=(-3.9)^{2}=15.21$ $(6 - 8.9)^{2}=(-2.9)^{2}=8.41$ $(8 - 8.9)^{2}=(-0.9)^{2}=0.81$ $(9 - 8.9)^{2}=(0.1)^{2}=0.01$ $(11 - 8.9)^{2}=(2.1)^{2}=4.41$ $(14 - 8.9)^{2}=(5.1)^{2}=26.01$ $(15 - 8.9)^{2}=(6.1)^{2}=37.21$ $(15 - 8.9)^{2}=(6.1)^{2}=37.21$ $\sum_{i = 1}^{10}(x_{i}-8.9)^{2}=47.61+24.01+15.21+8.41+0.81+0.01+4.41+26.01+37.21+37.21 = 190.9$ $\sigma^{2}=\frac{190.9}{10}=19.09$

Step5: Calculate the standard - deviation

$\sigma=\sqrt{\sigma^{2}}=\sqrt{19.09}\approx4.37$

Answer:

Range: $13$ Mean: $8.9$ Variance: $19.09$ Standard deviation: $\approx4.37$