# 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 | f_{i}x_{i} |
x_{i}² |
f_{i}x_{i}² |

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_{i}x_{i}

= 50/25

= 2

(σ²) = 1/N √ [N ∑ f_{i}x_{i}² - (∑ f_{i}x_{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

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

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