# NCERT Class 10 Chapter 14 Statistics CBSE Board Sample Problems Short Answer (For CBSE, ICSE, IAS, NET, NRA 2023)

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## Question

**If the mean of the following distribution is 54, find the missing frequency X**:

Class | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 |

Frequency | 16 | 14 | 24 | 26 | x |

### Solution

Class Interval | |||

0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 | 10 30 50 70 90 | 16 14 24 26 x | 160 420 1200 1820 90x |

Total | 80 + x | 3600 + 90x |

Mean

## Question

**The following table shows the distribution of weights of 100 candidates appearing for a competition. Determine the modal weight**.

Weight (in kg) | 50 - 55 | 55 - 60 | 60 - 65 | 65 - 70 | 70 - 75 | 75 - 80 |

No. of candidates | 13 | 18 | 45 | 16 | 6 | 2 |

### Solution

Class Interval | |

50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 75 - 80 | 13 18 45 16 6 2 |

Hear

Mode

## Question

**Sonic students of Class X donated for the welfare of old age persons. Their contributions are shown in the following frequency distribution**:

Amount (in ₹) | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 |

No. of students | 5 | 8 | 12 | 11 | 4 |

Find median and mode for their contribution.

### Solution

Median

For mode modal class 40 - 60

Mode

Number of students | c. f. | |

0 - 20 20 - 40
60 - 80 80 - 100 | 5 8
11 4 | 5 13
36 40 |

## Question

**The average score of boys in the examination of a school is 71 and that of the girls is 73. The average score of the school in the examination is 71.8. Find the ratio of the number of boys to the number of girls who appeared in the examination**.

### Solution

Let number of boys in the school be x

Average score of boys = 71

Total score of boys in the examination of the school

Let number of girls in the school be y

Average score of girls = 73

Total score of girls in the examination of the school

Now, average score of the school in examination

## Question

**The following data gives the information on the observed life times (in hours) of 150 electrical components**

Life time (in hours) | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 | 0 - 20 | 20 - 40 |

Frequency | 15 | 10 | 35 | 50 | 40 |

### Solution

Life time (in hours) | Frequency |

0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 | 15 10 35 50 Model Class 40 |

Model class is 60 - 80

Mode

## Question

**Determine the missing frequency x, from the following data when Mode is 67**.

Class | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 |

frequency | 5 | x | 15 | 12 | 7 |

### Solution

Class interval | Frequency |

40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 | 5 Modal class 7 |

Mode = 67 given

Model class is 60 - 70

Mode

## Question

**Find the unknown values in the following table**:

Class interval | Frequency | Cumulative Frequency |

0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 | 5 7 5 | 5 18 30 |

### Solution

Class interval | Frequency | Cumulative Frequency |

0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 | 5 7 5 | 5 18 30 |

From table:

## Question

**The mode of a distribution is 55 & the modal class is 45 - 60 and the frequency preceding the modal class is 5 and the frequency after the modal class is 10. Find the frequency of the modal class**

### Solution

Mode = 55

Modal class

Class preceding modal class

Class succeeding modal class

Mode

## Question

**Find the mean of 30 numbers given mean often of them is 12 and the mean of remaining 20 is 9**.

### Solution

Total number of mean = 30

Mean of 10 is = 12

Mean of 20 numbers is = 9

By (1) + (2)

Mean of 20 numbers =

10

## Question

**The mean of 5 numbers is 10. If 3 decrease each number, find the mean of the new number**.

### Solution

Mean of 5 nos

Since, each number is decreased by 3, then the sum is decreased by

Mean of new no

## Question

**The median of a data is 20. If each item is increased by 2, find the new median**.

### Solution

Median is the middle most item and each item is increased by 2, the new median will be

## Question

**The mean of 20 observations is 12. If each observation is increased by 5, then find the new mean**.

### Solution

If each observation is increased by 5 then the required new mean is also increased by 5.

Thus, the new mean is 17.

## Question

**The mean of 6**, **and** **Find the value of x**

### Solution

Mean

## Question

**Find the Mode of the following data**:

Class Intervals 10 – 14 15 - 19 20 - 24 25 - 29 30 - 34 35 - 39

Frequencies 30 45 75 35 25 10

Also, if the Median of the distribution is 20.8, find the Mean.

### Solution

Modal class is

Mode

Using Empirical formula

3 median