Question 1: Define cumulative frequency distribution.

Answer:

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 table.

Cumulative frequency distributions are of two types viz. less than and greater than or more than. For less than cumulative frequency distributions we add up the frequencies from the above and for greater than cumulative frequencies we add up the frequencies from below.

Question 2: Explain the difference between a frequency distribution and a cumulative frequency distribution.

Answer:

Frequency Distribution: Frequency distribution in statistics provides the information of the number of occurrences (frequency) of distinct values distributed within a given period of time or interval, in a list, table, or graphical representation.

Frequency distributions are of two types:

(i) Discrete frequency distribution (ii) Continuous or grouped frequency distribution

Cumulative frequency distribution: Refer to the above question.

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.

Answer:

Less than cumulative frequency

Marks | Cumulative Frequency |

Less than 5 | 2 |

Less than 10 | 8 |

Less than 15 | 21 |

Less than 20 | 38 |

Less than 25 | 49 |

Less than 30 | 53 |

Less than 35 | 55 |

More than cumulative frequency table

Marks | Cumulative Frequency |

More than 0 | 55 |

More than 4 | 53 |

More than 9 | 47 |

More than 14 | 34 |

More than 19 | 17 |

More than 24 | 6 |

More than 29 | 2 |

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 | 40-40 | 50-60 | 60-70 |

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

Construct a cumulative frequency distribution.

Answer:

Less than cumulative frequency

Marks | Cumulative Frequency |

Less than 20 | 90 |

Less than 30 | 140 |

Less than 40 | 200 |

Less than 50 | 280 |

Less than 60 | 330 |

Less than 70 | 360 |

More than cumulative frequency table

Marks | Cumulative Frequency |

More than 10 | 360 |

More than 19 | 270 |

More than 29 | 220 |

More than 39 | 160 |

More than 49 | 80 |

More than 59 | 30 |

Question 5: The water bills (in rupees) of 32 houses in a certain street for the period 1.1.98 to 31.3.98 are given below:

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

Answer:

First understand the frequency distribution. Arrange the given data in ascending order. Which is:

Hence, we get

Class Interval | Frequency |

20-29 | 2 |

30-39 | 6 |

40-49 | 5 |

50-59 | 7 |

60-69 | 6 |

70-79 | 3 |

80-89 | 2 |

90-99 | 1 |

Less than cumulative frequency

Water Bill | Cumulative Frequency |

Less than 30 | 2 |

Less than 40 | 8 |

Less than 50 | 13 |

Less than 60 | 20 |

Less than 70 | 26 |

Less than 80 | 29 |

Less than 90 | 31 |

Less than 100 | 32 |

More than cumulative frequency table

Marks | Cumulative Frequency |

More than 19 | 32 |

More than 29 | 30 |

More than 39 | 24 |

More than 49 | 19 |

More than 59 | 12 |

More than 69 | 6 |

More than 79 | 3 |

More than 89 | 1 |

Question 6: The number of books in different shelves of a library are as follows:

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

Answer:

First arrange the data in ascending order:

Hence, we get

Class Interval | Frequency |

15-19 | 5 |

20-24 | 13 |

25-29 | 17 |

30-34 | 13 |

35-39 | 7 |

40-44 | 4 |

45-49 | 1 |

Less than cumulative frequency

Water Bill | Cumulative Frequency |

Less than 20 | 5 |

Less than 25 | 18 |

Less than 30 | 35 |

Less than 35 | 48 |

Less than 40 | 55 |

Less than 45 | 59 |

Less than 50 | 60 |

More than cumulative frequency table

Marks | Cumulative Frequency |

More than 14 | 60 |

More than 19 | 55 |

More than 24 | 42 |

More than 29 | 25 |

More than 34 | 12 |

More than 39 | 5 |

More than 44 | 1 |

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 25 | 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 |

Answer:

Weight | No. of Students |

25-30 | 24 |

30-35 | 54 |

35-40 | 105 |

40-45 | 111 |

45-50 | 114 |

50-55 | 135 |

55-60 | 78 |

60-65 | 53 |

65-70 | 11 |

Question 8: The following cumulative frequency distribution table shows the daily electricity consumption (in kVV) 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 |

(i) Represent this as a frequency distribution table.

(ii) Prepare a cumulative frequency table.

Answer:

Consumption in kW | No. of families |

0-240 | 1 |

240-270 | 3 |

270-300 | 4 |

300-330 | 16 |

330-360 | 9 |

360-390 | 5 |

390-420 | 2 |

Consumption in kW | No. of families |

More than 0 | 40 |

More than 240 | 39 |

More than 270 | 36 |

More than 300 | 32 |

More than 330 | 16 |

More than 360 | 7 |

More than 390 | 2 |

More than 420 | 0 |

Question 9: Given below is a cumulative frequency distribution table showing the ages of people living in a locality:

Age in Years | No. of persons |

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.

Answer:

Age in years | No of persons |

0-12 | 98 |

12-24 | 217 |

24-36 | 382 |

36-48 | 269 |

48-60 | 138 |

60-72 | 15 |

72-84 | 2 |

84-96 | 2 |

96-108 | 1 |