#### Exercise 23.2

Q1. 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.

Answer: 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 |

5-10 | IIII IIII | 9 |

10-15 | IIII II | 7 |

15-20 | IIII IIII | 9 |

20-25 | IIII I | 6 |

Q2. 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?

Answer:

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.

Q3. 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?

Answer:

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

(ii) Class mark for the class 40-50:

\(\frac{40 + 50}{ 2 }\)

Again, class mark for the class 50-60:

\(\frac{50 + 60}{ 2 }\)

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

Q4. 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?

Answer:

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:

Class mark= \(\frac{40 + 45}{ 2 } = \frac{ 85 }{ 2 }\)

(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).

Q5. 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.

Answer:

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 |

5-10 | IIII | 5 |

10-15 | 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 |

Q6. 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.

Answer: 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 |

Q7. 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.

Answer:

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 |

Q8. 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.

Answer:

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 |

Q9. 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.

Answer:

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 |

Q10. 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.

Answer:

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 |