Data Handling I (Classification and Tabulation of Data) Exercise 23.2

Question: 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 for the marks of 40 students of class VIII in an examination is given below:

Range of Marks	Tally Marks	Frequency
0-5	IIII IIII	9
10-May	IIII IIII	9
15-Oct	IIII II	7
15-20	IIII IIII	9
20-25	IIII I	6

Question: 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:

(Marks in class interval)	Tally marks	Frequency (No. of Children)
40 – 50
50 – 60
60 – 70
70 – 80
80 – 90

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

Solution:

The frequency table can be completed as follows:

Marks	Tally Marks	Frequency
40-50	IIII	4
50-60	IIII III	8
60-70	III	3
70-80	III	3
80-90	II	2

The class interval with the greatest frequency (8) is 50-60.

 

Question: 3

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

Weight in kg	Persons
30-40	10
40-50	15
50-60	17
60-70	6
70-80	4

(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) Class mark for the class 40-50:

(iii) Here the class size is 40-30, i.e. 10.

 

Question: 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 for the given weights (in gm) of 35 mangoes is given below:

Weight	Tally Marks	Frequency
30-40	IIII I	6
40-50	IIII I	6
50-60	IIII IIII	9
60-70	IIII II	7
70-80	IIII II	7

(i) Class mark for the class interval 40 – 45:

(ii) Range of the above weights:

Range = Highest value-Lowest value

= 74 – 30 = 44

(iii)There are 5 classes (30-40, 40-50, 50-60, 60-70, 70-80).

 

Question: 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 with class intervals 0 – 5, 5 – 10, 10 – 15, . . . , 50 – 55 is given below:

Marks	Tally Marks	Frequency
0-5	III	3
43230	IIII	5
43388	III	3
15-20	IIII	5
20-25	III	3
25-30	III	3
30-35	I	1
35-40	II	2
40-45	II	2
45-50	II	2
50-55	I	1

Question: 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 the class size of 10 marks.

Solution:

The frequency table of the marks scored by 40 students of class VIII in mathematics is given below:

Mark	Tally Marks	Frequency
20-30	I	1
30-40	III	3
40-50	IIII	5
50-60	IIII III	8
60-70	IIII III	8
70-80	III	9
80-90	IIII	4
90-100	II	2

Question: 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 table is given below:

Height	Tally Marks	Frequency
145-149	IIII	4
150-154	IIII IIII	9
155-159	IIII IIII II	12
160-164	IIII	5

Question: 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 is given below:

Wage	Tally Marks	Frequency
800-810	III	3
810-820	II	2
820-830	I	1
830-840	IIII III	8
840-850	IIII	5
850-860	I	1
860-870	III	3
870-880	I	1
880-890	I	1
890-900	IIII	5

Question: 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 is given below:

Wage	Tally Marks	Frequency
210-230	IIII	4
230-250	IIII	4
250-270	IIII	5
270-290	III	3
290-310	IIII II	7
310-330	IIII	5

Question: 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 is given below:

Temperature	Tally Marks	Frequency
-19.9 to -15	I	1
-14.9 to -10	IIII IIII	8
-9.9 to -5	IIII	5
-4.9 to 0	IIII IIII III	13
0.1 to 5	IIII III	8