In Exercise 23.2, we shall follow an algorithm which is used to construct a grouped frequency distribution. For all these problems, RD Sharma Class 8 Solutions contain solutions which fulfil all student requirements. For further reference to the solutions of this exercise, the RD Sharma Class 8 Maths Chapter 23 is available in the PDF format, which can be accessed offline. Students can download the PDF from the links given below.
Download the PDF of RD Sharma Solutions for Class 8 Maths Exercise 23.2 Chapter 23 Data Handling – I (Classification and Tabulation of Data)
Access answers to RD Sharma Maths Solutions For Class 8 Exercise 23.2 Chapter 23 Data Handling – I (Classification and Tabulation of Data)
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 shown below:
| Range of Marks | No: of Students |
| 0-5 | 9 |
| 5-10 | 9 |
| 10-15 | 7 |
| 15-20 | 9 |
| 20-25 | 6 |
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:
Â
What is the class interval in which the greatest frequency occurs?
Solution:
The frequency table can be completed as follows:
| Marks in Class Interval | Tally Marks | No: of Children |
| 40 – 50 | IIII | 4 |
|
 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.
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:
i.e., (40+50) / 2 = 90/2 = 45
Again, Class mark for the class 50-60:
i.e., (50+60) / 2 = 110/2 = 55
(iii) Here the class size is 40-30, i.e. 10.
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:
| Weight (in grams) | No: of Mangoes |
| 30 – 35 | 5 |
| 35 – 40 | 2 |
| 40 – 45 | 4 |
| 45 – 50 | 3 |
| 50 – 55 | 5 |
| 55 – 60 | 3 |
| 60 – 65 | 5 |
| 65 – 70 | 5 |
| 70 – 75 | 3 |
(i) Class mark for the class interval 40 – 45:
Class mark = (40+45) / 2 = 85/2 = 42.5
(ii) Range of the above weights:
Range = Highest value – Lowest value
Range = 74 – 30 = 44
(iii) Number of classes = 9
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, . . . , 45 – 50 is shown below:
| Marks | No: of Students |
| 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 |
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 is shown below:
| Marks | Frequency Distribution |
| 20 – 30 | 1 |
| 30 – 40 | 3 |
| 40 – 50 | 5 |
| 50 – 60 | 8 |
| 60 – 70 | 9 |
| 70 – 80 | 8 |
| 80 – 90 | 34 |
| 90 – 100 | 2 |
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 is shown below:
| Height (in cm) | No: of Students |
| 145 – 149 | 4 |
| 150 – 154 | 9 |
| 155 – 159 | 12 |
| 160 – 164 | 5 |
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 shown below:
| Wages | No: of Workers |
| 800 – 809 | 3 |
| 810 – 819 | 2 |
| 820 – 829 | 1 |
| 830 – 839 | 8 |
| 840 – 849 | 5 |
| 850 – 859 | 1 |
| 860 – 869 | 3 |
| 870 – 879 | 1 |
| 880 – 889 | 1 |
| 890 – 899 | 5 |
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 shown below:
| Wages | No: of Workers |
| 210 – 230 | 4 |
| 230 – 250 | 4 |
| 250 – 270 | 5 |
| 270 – 290 | 3 |
| 290 – 310 | 7 |
| 310 – 330 | 5 |
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 shown below:
| Temperature | Frequency Distribution |
| –19.9 to –15 | 1 |
| –15 to –11.1 | 6 |
| –11.1 to –6.2 | 6 |
| –6.2 to –1.3 | 9 |
| –1.3 to 3.6 | 13 |
Comments