**Chapter 22: Tabular Representation of Statistical Data Exercise – 22.2**

**Question: 1**

Define cumulative frequency distribution.

**Solution:**

Cumulative frequency distribution:

A table which displays the manner in which cumulative frequencies are distributed over various classes is called a cumulative frequency distribution or cumulative frequency distribution table.

**Question: 2**

Explain the difference between a frequency distribution and a cumulative frequency distribution.

**Solution:**

Frequency table or frequency distribution is a method to represent raw data in the form from which one can easily understand the information contained in a raw data, where as a table which plays the manner in which cumulative frequencies are distributed over various classes is called a cumulative frequency distribution.

**Question: 3**

The marks scored by 55 students in a test are given below:

Marks |
0 – 5 | 5 – 10 | 10 – 15 | 15 – 20 | 20 – 25 | 25 – 30 | 30 – 35 |

No. of students |
2 | 6 | 13 | 17 | 11 | 4 | 2 |

Prepare a cumulative frequency table

**Solution:**

Marks |
No. of Students |
Marks |
Cumulative Frequency |

0 – 5 | 2 | Less than 5 | 2 |

5 – 10 | 6 | Less than 10 | 8 |

10 – 15 | 13 | Less than 15 | 21 |

15 – 20 | 17 | Less than 20 | 38 |

20 – 25 | 11 | Less than 25 | 49 |

25 – 30 | 4 | Less than 30 | 53 |

30 – 35 | 2 | Less than 35 | 55 |

N = 55 |

**Question: 4**

Following are the ages of 360 patients getting medical treatment in a hospital on a day.

Age (in years) |
10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 | 60 – 70 |

No of Patients |
90 | 50 | 60 | 80 | 50 | 30 |

Construct a cumulative frequency table.

**Solution:**

Age (in years) |
No. of students |
Marks |
Cumulative Frequency |

10 – 20 | 90 | Less than 20 | 90 |

20 – 30 | 50 | Less than 30 | 140 |

30 – 40 | 60 | Less than 40 | 200 |

40 – 50 | 80 | Less than 50 | 280 |

50 – 60 | 50 | Less than 60 | 330 |

60 – 70 | 30 | Less than 70 | 360 |

N = 360 |

**Question: 5**

The water bills (in rupees) of 32 houses in a certain street for the period 1.198 to 31.398 are given below:

56, 43, 32, 38, 56, 24, 68, 85, 52, 47, 35, 58, 63, 74, 27, 84, 69, 35, 44, 75, 55, 30, 54, 65, 45, 67, 95, 72, 43, 65, 35, 69.

Tabulate the data and present the data as a cumulative frequency table using 70-79 as one of the class intervals.

**Solution:**

The minimum bill is Rs 24

The maximum bill is Rs 95

Range = Maximum bill-Minimum bill = 95 - 24 = 71

Given class interval is 70-79. So, Class size = 79 – 70 = 9

Therefore number of classes = Range/class size = 71/9 = 7.80

Number of classes = 8

The cumulative frequency distribution is as follows:

Bills |
No. of Houses (Frequency) |
Cumulative Frequency |

16 – 25 | 1 | 1 |

25 – 34 | 3 | 4 |

34 – 43 | 5 | 9 |

43 – 52 | 4 | 13 |

52 – 61 | 7 | 20 |

61 – 70 | 6 | 26 |

70 – 79 | 3 | 29 |

79 – 88 | 2 | 31 |

88 – 97 | 1 | 32 |

**Question: 6**

The number of books in different shelves of a library is as follows:

30, 32, 28, 24, 20, 25, 38, 37, 40, 45, 16, 20

19, 24, 27, 30, 32, 34, 35, 42, 27, 28, 19, 34

38, 39, 42, 29, 24, 27, 22, 29, 31, 19, 27, 25

28, 23, 24, 32, 34, 18, 27, 25, 37, 31, 24, 23

43, 32, 28, 31, 24, 23, 26, 36, 32, 29, 28, 21.

Prepare a cumulative frequency distribution table using 45 – 49 as the last class-interval.

**Solution:**

The minimum number of bookshelves is 16

and maximum number of bookshelves is 45

Range = Maximum book shelves-Minimum book shelves = 45 - 16 = 29

Given class interval is 45 – 49.So, class size = 49 - 45 = 4

Therefore number of classes = Range/class size = 29/4 = 7.25

Number of classes = 8

The cumulative frequency distribution is as follows:

No of Books |
No. of Shelves (Frequency) |
Cumulative Frequency |

13 – 17 | 1 | 1 |

17 – 21 | 6 | 7 |

21 – 25 | 11 | 18 |

25 – 29 | 15 | 33 |

29 – 33 | 12 | 45 |

33 – 37 | 5 | 50 |

37 – 41 | 6 | 56 |

41 – 45 | 3 | 59 |

45 – 49 | 1 | 60 |

**Question: 7**

Given below are the cumulative frequencies showing the weights of 685 students of a school. Prepare a frequency distribution table.

Weight (in kg) |
No. of students |

Below 30 | 0 |

Below 30 | 24 |

Below 35 | 78 |

Below 40 | 183 |

Below 45 | 294 |

Below 50 | 408 |

Below 55 | 543 |

Below 60 | 621 |

Below 65 | 674 |

Below 70 | 685 |

**Solution:**

Weight (in kg) |
No. of students |
Class interval |
frequency |

Below 30 | 24 | 25 – 30 | 24 – 0 = 24 |

Below 35 | 78 | 30 – 35 | 78 – 24 = 54 |

Below 40 | 183 | 35 – 40 | 183 – 78 = 105 |

Below 45 | 294 | 40 – 45 | 294 – 183 = 111 |

Below 50 | 408 | 45 – 50 | 408 – 294 = 114 |

Below 55 | 543 | 50 – 55 | 543 – 408 = 135 |

Below 60 | 621 | 55 – 60 | 621 – 543 = 78 |

Below 65 | 674 | 60 – 65 | 671 – 621 = 53 |

Below 70 | 685 | 65 – 70 | 685 – 671 = 11 |

**Question: 8**

The following cumulative frequency distribution table shows the daily electricity consumption (in KW) of 40 factories in an industrial state.

Consumption (in KW) |
No. of factories |

Below 240 | 1 |

Below 270 | 4 |

Below 300 | 8 |

Below 330 | 24 |

Below 360 | 33 |

Below 390 | 38 |

Below 420 | 40 |

(1) Represent this as a frequency distribution table.

(2) Prepare a cumulative frequency table.

**Solution:**

(1)

Consumption(in KW) |
No. of factories |
Class interval |
Frequency |

Below 240 | 1 | 0 – 240 | 1 |

Below 270 | 4 | 240 – 270 | 4 – 1 = 3 |

Below 300 | 8 | 270 – 300 | 8 – 4 = 4 |

Below 330 | 24 | 300 – 330 | 24 – 8 = 16 |

Below 360 | 33 | 330 – 360 | 33 – 24 = 9 |

Below 390 | 38 | 360 – 390 | 38 – 33 = 5 |

Below 420 | 40 | 390 – 420 | 40 – 38 = 2 |

(2)

Class interval |
Frequency |
Consumption(in KW) |
No. of factories |

0 – 240 | 1 | More than 0 | 40 |

240 – 270 | 3 | More than 240 | 40 – 1 = 39 |

270 – 300 | 4 | More than 270 | 39 – 3 = 36 |

300 – 330 | 16 | More than 300 | 36 – 4 = 32 |

330 – 360 | 9 | More than 330 | 32 – 16 = 16 |

360 – 390 | 5 | More than 360 | 16 – 9 = 7 |

390 – 420 | 2 | More than 390 | 7 – 5 = 2 |

More than 420 | 2 – 2 = 0 | ||

N = 40 |

**Question: 9**

Given below is a cumulative frequency distribution table showing ages of the people living in a locality:

Age in years |
No. of years |

Above 108 | 0 |

Above 96 | 1 |

Above 84 | 3 |

Above 72 | 5 |

Above 60 | 20 |

Above 48 | 158 |

Above 36 | 427 |

Above 24 | 809 |

Above 12 | 1026 |

Above 0 | 1124 |

Prepare a frequency distribution table.

**Solution:**

Age (in years) |
No. of persons |
Class interval |
Frequency |

Above 0 | 1124 | 0 – 12 | 1124 – 1026 = 98 |

Above 12 | 1026 | 12 – 24 | 217 |

Above 24 | 809 | 24 – 36 | 382 |

Above 36 | 427 | 36 – 48 | 269 |

Above 38 | 158 | 48 – 60 | 138 |

Above 60 | 20 | 60 – 72 | 15 |

Above 72 | 5 | 72 – 84 | 5 – 3 = 2 |

Above 84 | 3 | 84 – 96 | 3 – 1 = 2 |

Above 96 | 3 | 96 – 108 | 1 – 0 = 1 |