Class 8 RD Sharma Solutions Chapter 23 Data Handling I (Classification And Tabulation Of Data) Exercise 23.2 (original) (raw)

Last Updated : 21 Feb, 2021

Problem 1: The marks obtained by 40 students of class VIII in an examination are given below:

16, 17, 18, 3, 7, 23, 18, 13, 10, 21, 7, 1, 13, 21, 13, 15, 19, 24, 16, 3, 23, 5, 12, 18, 8, 12, 6, 8, 16, 5, 3, 5, 0, 7, 9, 12, 20, 10, 2, 23.

Divide the data into five groups namely 0-5, 5-10, 10-15, 15-20, and 20-25, and prepare a grouped frequency table.

Solution:

The frequency table of the marks of 40 students of class VIII in an examination can be shown as -

Range of marks (class-interval)	Tally marks	Number of students (frequency)
0-5	~~|
5-10	~~|
10-15	~~|
15-20	~~|
20-25	~~|

Problem 2: The marks scored by 20 students in a test are given below:

54, 42, 68, 56, 62, 71, 78, 51, 72, 53, 44, 58, 47, 64, 41, 57, 89, 53, 84, 57.

Complete the following frequency table :

What is the class interval in which the greatest frequency occurs?

Solution:

The frequency table can be completed as -

(Marks in class intervals)	Tally marks	Frequency (Number of children)
40-50	|
50-60	~~|
60-70	|
70-80	|
80-90	|		2

The class interval with the greatest frequency is 50-60.

Problem 3: The following is the distribution of weights (in kg) of 52 persons:

(i) What is the lower limit of class 50-60?

(ii) Find the class marks of the classes 40-50, 50-60.

(iii) What is the class size?

Solution:

(i) The lower limit of the class 50-60 is 50.

(ii) The class mark for the class 40-50 = (40 + 50)/ 2 = 90/2 = 45

and the class mark for the class 50-60 = (50 + 60)/ 2 = 110/2 = 55

(iii) The class size is 40-30 = 10.

Problem 4: Construct a frequency table for the following weights (in gm) of 35 mangoes using the equal class intervals, one of them is 40-45 (45 not included):

30, 40, 45, 32, 43, 50, 55, 62, 70, 70, 61, 62, 53, 52, 50, 42, 35, 37, 53, 55, 65, 70, 73, 74, 45, 46, 58, 59, 60, 62, 74, 34, 35, 70, 68.

(i) What is the class mark of the class interval 40-45?

(ii) What is the range of the above weights?

(iii) How many classes are there?

Solution:

The frequency table of the given weights of 35 mangoes using the equal class intervals and one of the class intervals as 40-45

(45 not included) can be shown as -

Weight (in grams)	Tally marks	Number of mangoes (frequency)
30-35	|
35-40	|
40-45	|
45-50	|
50-55	~~|
55-60	|
60-65	~~|
65-70	|		2
70-75	~~|

(i) The class mark for the class interval 40-45 = (40 + 45)/ 2 = 85/2 = 42.5

(ii) The range of the above weights = Highest value – Lowest value = 74 – 30 = 44

(iii) The number of classes = 9

Problem 5: Construct a frequency table with class-intervals 0-5 (5 not included) of the following marks obtained by a group of 30 students in an examination:

0, 5, 7, 10, 12, 15, 20, 22, 25, 27, 8, 11, 17, 3, 6, 9, 17, 19, 21, 29, 31, 35, 37, 40, 42, 45, 49, 4, 50, 16.

Solution:

The frequency table of marks obtained by a group of 30 students in an examination with class-intervals 0-5 (5 not included) can

be shown as -

Marks (class-interval)	Tally marks	Number of students (frequency)
0-5	|
5-10	~~|
10-15	|
15-20	~~|
20-25	|
25-30	|
30-35	|	1
35-40	|
40-45	|
45-50	|
50-55	|	1

Problem 6: The marks scored by 40 students of class VIII in mathematics are given below:

81, 55, 68, 79, 85, 43, 29, 68, 54, 73, 47, 35, 72, 64, 95, 44, 50, 77, 64, 35, 79, 52, 45, 54, 70, 83, 62, 64, 72, 92, 84, 76, 63, 43, 54, 38, 73, 68, 52, 54.

Prepare a frequency distribution with class size of 10 marks.

Solution:

The frequency table of the marks scored by 40 students of class VIII in mathematics can be shown as -

Marks (class-interval)	Tally marks	Number of students (frequency)
20-30	|	1
30-40	|
40-50	~~|
50-60	~~|
60-70	~~|
70-80	~~|
80-90	|
90-100	|		2

Problem 7: The heights (in cm) of 30 students of class VIII are given below:

155, 158, 154, 158, 160, 148, 149, 150, 153, 159, 161, 148, 157, 153, 157, 162, 159, 151, 154, 156, 152, 156, 160, 152, 147, 155, 163, 155, 157, 153.

Prepare a frequency distribution table with 160-164 as one of the class intervals.

Solution:

The frequency distribution table of the heights of 30 students of class VIII with 160-164 as one of the class intervals can be

shown as -

Height (in cm) (class-interval)	Tally marks	Number of students (frequency)
144-148	|	1
148-152	~~|
152-156	~~|
156-160	~~|
160-164	~~|

Problem 8: The monthly wages of 30 workers in a factory are given below:

830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 836, 878, 840, 868, 890, 806, 840, 890.

Represent the data in the form of a frequency distribution with class size 10.

Solution:

The frequency table of the monthly wages of 30 workers in a factory can be shown as -

Wages (class-interval)	Tally marks	Number of workers (frequency)
800-810	|
810-820	|		2
820-830	|	1
830-840	~~|
840-850	~~|
850-860	|	1
860-870	|
870-880	|	1
880-890	|	1
890-900	~~|

Problem 9: Construct a frequency table with equal class intervals from the following data on the monthly wages (in rupees) of 28 labourers working in a factory, taking one of the class intervals as 210-230 (230 not included) :

220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 304, 302, 318, 306, 292, 254, 278, 210, 240, 280, 316, 306, 215, 256, 236.

Solution:

The frequency table of the monthly wages of 28 laborers working in a factory, taking one of the class intervals as 210-230

(230 not included) can be shown as -

Wages (in rupees) (class-interval)	Tally marks	Number of workers (frequency)
210-230	|
230-250	|
250-270	~~|
270-290	|
290-310	~~|
310-330	~~|

Problem 10: The daily minimum temperatures in degrees Celsius recorded in a certain Arctic region are as follows :

-12.5, -10.8, -18.6, -8.4, -10.8, -4.2, -4.8, -6.7, -13.2, -11.8, -2.3, 1.2, 2.6, 0, -2.4, 0, 3.2, 2.7, 3.4, 0, -2.4, -2.4, 0, 3.2, 2.7, 3.4, 0, -2.4, -5.8, -8.9, -14.6, -12.3, -11.5, -7.8, -2.9

Represent them as frequency distribution table taking -19.9 to -15 as the first class interval.

Solution:

The frequency table of the daily minimum temperatures taking -19.9 to -15 as the first class interval can be shown as -

Temperature (class-interval)	Tally marks	Frequency
-19.9 to -15	|	1
-15 to -10.1	~~|
-10.1 to -5.2	~~|
-5.2 to -0.3	~~|
-0.3 to 4.6	~~|