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RD Chapter 22 Tabular Representation of Statistical Data Ex 22.2 Solutions

Question - 1 : - Define cumulative frequency distribution.

Answer - 1 : - Cumulative frequency : In a discrete frequency distribution, the cumulative frequency of a particular value of the variable is the total of all the frequencies of the values of the variable which are less than or equal to the particular value.

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

Answer - 2 : -

The number of times an observation occurs in the given data, is called frequency of the
observation while a cumulative frequency of a particular value of the variable is the total of all the frequencies of the values of the variable which are less than or equal to the particular value.

Question - 3 : -
The marks scored by 55 students in a test are given below:
 
Prepare a cumulative frequency table.

Answer - 3 : - Cumulative frequency table is given below:

Question - 4 : -
Following are the ages of 360 patients getting medical treatment in a hospital on a day:
 
Construct a cumulative frequency distribution.

Answer - 4 : - Cumulative frequency distribution table (less than) is given below:

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:
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, 59.
Tabulate the data and present the data as a cumulative frequency table using 70-79 as one of the class intervals.

Answer - 5 : -

Highest bill = 95 Lowest bill = 24
Range = 95 – 24 = 71
Cumulative frequency table is given below:

Question - 6 : -
The number of books in different shelves of a library are 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.

Answer - 6 : -

Greatest number = 43
Lowest number =16
Range = 43 – 16 = 27
Cumulative frequency table is given below:

Question - 7 : - Given below are the cumulative frequencies showing the weights of 685 students of a school. Prepare a frequency distribution table.

Answer - 7 : - The frequency table of the given cumulative frequency is given below:

Question - 8 : -
The following cumulative frequency distribution table shows the daily electricity consumption (in kW) of 40 factories in an industrial state:
 
(i) Represent this as a frequency distribution table.
(ii) Prepare a cumulative frequency table.

Answer - 8 : -

(i) The frequency distribution table is given below:
 
(ii) Now cumulative frequency table (more then)

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

Answer - 9 : - Frequency distribution table is given below:

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