The document RD Sharma Solutions -Ex-22.2, Tabular Representation Of Statistical Data, Class 9, Maths Class 9 Notes | EduRev is a part of the Class 9 Course RD Sharma Solutions for Class 9 Mathematics.

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**Q1. Define cumulative frequency distribution.**

**Solution 1: ****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.

**Q2. Explain the difference between a frequency distribution and a cumulative frequency distribution.**

**Solution 2:**

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.

**Q3. 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 3:**

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 | |

**Q4. 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 4:**

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 | | |

**Q5. 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 5:**

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 =

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 |

**Q6.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 6:**

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 =

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 |

**Q7. 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 7:**

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 |

**Q8. 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 8:**

**(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 | | |

**Q9. 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 9:**

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 |

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