Answer:
(a)The mean scores for Team A and B are 7.9 and 10.6 respectively.
(b)Variance for Team A scores =29.49
(c)Standard deviation for Team A scores = 5.43
Explanation:
The points scored per player in each team is:
• Team A: 6,2,8,10,3,15,4,20,7,4
,
• Team B: 5,9,7,9,13,11,13,15,14,10
Part A
We find the mean by adding all the points and dividing by the number of players 10.
[tex]\begin{gathered} \text{Mean Points for Team A} \\ =\frac{6+2+8+10+3+15+4+20+7+4}{10}=\frac{79}{10} \\ =7.9 \end{gathered}[/tex]
Similarly:
[tex]\begin{gathered} \text{Mean Points for Team B} \\ =\frac{5+9+7+9+13+11+13+15+14+10}{10}=\frac{106}{10} \\ =10.6 \end{gathered}[/tex]
The mean scores for Team A and B are 7.9 and 10.6 respectively.
Part B (Variance for Team A)
To calculate the variance, we make use of the formula below:
[tex]\sigma^2=\frac{\sum_{i=1}^{n}\left(x_{i}-\mu\right)^{2}}{n}[/tex]
Using the table below:
Therefore:
[tex]\begin{gathered} \text{Variance,}\sigma^2=\frac{\sum^n_{i=1}(x_i-\mu)^2}{n}=\frac{294.9}{10} \\ \sigma^2=29.49 \end{gathered}[/tex]
The variance of Team A scores is 29.49.
Part C (Standard deviation of Team A scores)
The standard deviation is the square root of the variance.
From part (B), variance = 29.49
Therefore:
[tex]\sigma=\sqrt[]{29.49}=5.43[/tex]
The standard deviation of Team A scores is 5.43.
