The following is the record of goals scored ...

NCERT Class XI Mathematics - Statistics - Solutions

Question : 26 of 34

Marks: +1, -0

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?

Solution:

For team A :

$x_i$	$f_i$	$f_i x_i$	$f_i x_i^2$
0	1	0	0
1	9	9	9
2	7	14	28
3	5	15	45
4	3	12	48
	25	50	130

Mean

(\overline{x_A})

\frac{1}{N} \sum f_i x_i

\frac{1}{25}

× 50 = 2 ; S.D.

(\sigma_A)

\sqrt{ \frac{ \sum f_i x_i^2 }{ N } - \left( \frac{ \sum f_i x_i }{ N } \right)^2 }

\sqrt{ \frac{130}{25} - \left( \frac{50}{25} \right)^2 }

\sqrt{5.2 - 4}

\sqrt{1.2}

= 1.09

∴ C.V. of team A =

\frac{1.09}{2}

× 100 = 54.5

C.V. of team B=

\frac{1.25}{2}

× 100 = 62.5

Since C.V. of team A < C.V. of team B. Thus team A is more consistent.

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