# 4.  The following is the record of goals scored by team A in a football session: No. of goals scored 0 1 2 3 4 No. of matches 1 9 7 5 3 For the team B, mean number of goals scored per match was 2 with a standard deviation  $1.25$  goals. Find which team may be considered more consistent?

 No. of goals scored $x_i$ Frequency $f_i$ $x_i^2$ $f_ix_i$ $f_ix_i^2$ 0 1 0 0 0 1 9 1 9 9 2 7 4 14 28 3 5 9 15 45 4 3 16 12 48 $\sum{f_i}$ =N = 25 $\dpi{100} \sum f_ix_i$ = 50 $\dpi{100} \sum f_ix_i ^2$ =130

For Team A,

Mean,

$\overline{x} = \frac{1}{N}\sum_{i=1}^{n}f_ix_i =\frac{50}{25}= 2$

We know, Variance, $\sigma^2 = \frac{1}{N^2}\left [N\sum f_ix_i^2 - (\sum f_ix_i)^2 \right ]$

$\\ \implies \sigma^2 = \frac{1}{(25)^2}\left [25(130) - (50)^2 \right ] \\ \\ = \frac{750}{625} =1.2$

We know,  Standard Deviation = $\sigma = \sqrt{Variance}$

$\therefore \sigma = \sqrt{1.2} = 1.09$

C.V.(A) = $\frac{\sigma}{\overline x}\times100 = \frac{1.09}{2}\times100 = 54.5$

For Team B,

Mean = 2

Standard deviation, $\sigma$ = 1.25

C.V.(B) = $\frac{\sigma}{\overline x}\times100 = \frac{1.25}{2}\times100 = 62.5$

Since C.V. of firm B is more than C.V. of A.

Therefore, Team A is more consistent.

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