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 :
(Marks in class intervals) | Tally marks | Frequency (Number 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 –
(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:
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) 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 ||| 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
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