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?

Answers (1)

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

 

\sum f_ix_i

= 50

\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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