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 math was 2 with a standard deviation of 1.25 goals. Find which team may be considered more consistent?

Solution:

The mean and standard deviation of goals scored by team A is calculated as follows.

No. of goals scored	No. of matches	fixi	xi²	fixi²
0	1	0	0	0
1	9	9	1	9
0	1	0	0	0
1	9	9	1	9

Mean,

x = 1/N ∑⁵_{i = 1} f_ix_i

= 50/25

= 2

(σ²) = 1/N √  [N ∑ f_ix_i² - (∑ f_ix_i)²]

= 1/25 √ 25 x 130 - (50)²

= 1/25 √ 750

= 1/25 x 27.38

= 1.09

The standard deviation of team B is 1.25 goals.

The average number of goals scored by both the teams is the same i.e., 2.

Therefore, the team with a lower standard deviation will be more consistent.

Thus, team A is more consistent than team B

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NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.3 Question 4

The following is the record of goals scored by team A in a football session: For the team B, mean number of goals scored per math was 2 with a standard deviation of 1.25 goals. Find which team may be considered more consistent?

Summary:

From the given data, team A is more consistent than team B as team with a lower standard deviation will be more consistent