# Statistics

## Exercise 14.4

Question 1. The following number of goals were scored by a team in a series of 10 matches:

2, 3, 4, 5, 0, 1, 3, 3, 4, 3

Find the mean, median and mode of these scores.

**Answer:** Mean = Sum of observations ÷ Number of observations

= (2 + 3 + 4 + 5 + 0 + 1 + 3 + 3 + 4 + 3) ÷ 10

=28 ÷ 10 = 2.8

Question 2: In a mathematics test given to 15 students, the following marks (out of 100) are recorded:

41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60

Find the mean, median and mode of this data.

**Answer:** Mean = Sum of observations ÷ Number of observations

= (39 + 40 + 40 + 41 + 42 + 46 + 48 + 52 + 52 + 52 + 54 + 60 + 62 + 96 + 98) ÷ 15

`=(792)/(15)=52.8`

As there are odd number of observations so, Median `=(n+1)/2=(15+1)/2=9`

8th term = 52

Mode = The term with most frequency = 52

Question 3: The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.

29, 32, 48, 50, x, x + 2, 72, 78, 84, 95

**Answer:** Mean = 630 = (29 + 32 + 48 + 50 + x + x + 2 + 72 + 78 + 84 + 95) ÷ 10

Or, `630=490+2x`

Or, `2x=630–490=140`

Or, `x=70`

Question 4: Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.

**Answer:** Mode = term with most frequency = 14

Question 5: Find the mean salary of 60 workers of a factory from the following table:

Salary (in Rs.) | Number of workers |
---|---|

3000 | 16 |

4000 | 12 |

5000 | 10 |

6000 | 8 |

7000 | 6 |

8000 | 4 |

9000 | 3 |

10000 | 1 |

Total | 60 |

**Answer:**

Salary (in Rs.)(xi) | No. of workers (fi) | fixi |
---|---|---|

3000 | 16 | 48000 |

4000 | 12 | 48000 |

5000 | 10 | 50000 |

6000 | 8 | 48000 |

7000 | 6 | 42000 |

8000 | 4 | 32000 |

9000 | 3 | 27000 |

10000 | 1 | 10000 |

Total | `Σf_i = 60` | `Σf_i\x_i = 305000` |

`Me\an\=(Σf_i\x_i)/(Σf_i)=305000/60=5083.33`

Question 6: Give one example of a situation in which

(i) the mean is an appropriate measure of central tendency.

**Answer:** When data does not have extreme values then mean is an appropriate measure of central tendency.

(ii) the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency

**Answer:** When data has extreme values then median is an appropriate measure of central tendency.