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	|||| |	6
5-10	|||| ||||	10
10-15	|||| |||	8
15-20	|||| ||||	9
20-25	|||| ||	7

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	||||	4
50-60	|||| |||	8
60-70	|||	3
70-80	|||	3
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?

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	|||	3
35-40	|||	3
40-45	|||	3
45-50	|||	3
50-55	||||	5
55-60	||||	4
60-65	||||	5
65-70	||	2
70-75	|||| ||	7

(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	|||	3
5-10	||||	5
10-15	|||	3
15-20	||||	5
20-25	|||	3
25-30	|||	3
30-35	|	1
35-40	||	2
40-45	||	2
45-50	||	2
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	|||	3
40-50	||||	5
50-60	|||| |||	8
60-70	|||| ||||	9
70-80	|||| |||	8
80-90	||||	4
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	||||	5
152-156	|||| ||||	10
156-160	|||| ||||	9
160-164	||||	5

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	|||	3
810-820	||	2
820-830	|	1
830-840	|||| |||	8
840-850	||||	5
850-860	|	1
860-870	|||	3
870-880	|	1
880-890	|	1
890-900	||||	5

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	||||	4
230-250	||||	4
250-270	||||	5
270-290	|||	3
290-310	|||| ||	7
310-330	||||	5

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	|||| |||	8
-10.1 to -5.2	||||	5
-5.2 to -0.3	|||| |||	8
-0.3 to 4.6	|||| |||| |||	13