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Question

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?

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Solution

The given data is:

No. of goals scored01234
No. of matches19753

Make a table to calculate the mean and standard deviation of the given data.

No. of goals scored, x i No. of matches, f i f i x i ( x i ) 2 f i ( x i ) 2
01000
19919
2714428
3515945
43121648
i=1 n f i =25 i=1 n f i x i =50 i=1 n f i ( x i ) 2 =130

The formula to calculate the mean is,

x ¯ = i=1 n f i x i i=1 n f i = 1 N i=1 n f i x i (1)

Substitute 50 for i=1 n f i x i and 25 for N in equation (1).

x ¯ = 1 25 ( 50 ) =2

Therefore, the mean of the given data is 2.

The formula to calculate the standard deviation is,

σ= 1 N N i=1 n f i ( x i ) 2 ( i=1 n f i x i ) 2 (2)

Substitute 25 for N, 130 for i=1 n f i ( x i ) 2 and 50 for i=1 n f i x i in equation (2).

σ= 1 25 25( 130 ) ( 50 ) 2 = 1 25 750 = 27.38 25 =1.09

Thus, the standard deviation is 1.09.

It is given that the mean number of goals scored per match for team B is 2 and the standard deviation is 1.25. As it is seen that the mean for both the teams are the same, therefore the highest consistency is calculated by the least value of standard deviation. As team A has less standard deviation, therefore team A is more consistent.

Thus, team A is more consistent than team B.


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