Question

# Using the data in example (3) above, prepare less than type cumulative frequency table and answer the following questions. (i) How many students obtained less than 40 marks ? (ii) How many students obtained less than 10 marks ? (iii) How many students obtained less than 60 marks ? (iv) Find the cumulative frequency of the class 50-60.

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Solution

## Given: The data is given for 62 students in a certain class regarding their mathematics marks out of 100. 55, 60, 81, 90, 45, 65, 45, 52, 30, 85, 20, 10, 75, 95, 09, 20, 25, 39, 45, 50, 78, 70, 46, 64, 42, 58, 31, 82, 27, 11, 78, 97, 07, 22, 2 36, 35, 40, 75, 80, 47, 69, 48, 59, 32, 83, 23, 17, 77, 45, 05, 23, 37, 38, 35, 25, 46, 57, 68, 45, 47, 49. The frequency distribution table for the given data is as follows: Class (Marks obtained) Tally marks Frequency (No. of students) 0-10 ||||$||||$ 4 10-20 |||$|||$ 3 20-30 |||| ∣∣∣∣∣∣$\overline{)||||}|||$ 8 30-40 |||| ∣∣∣∣∣∣∣∣$\overline{)||||}||||$ 9 40-50 |||| |||| ∣∣∣∣∣∣$\overline{)||||}\overline{)||||}|||$ 13 50-60 |||| ∣∣$\overline{)||||}|$ 6 60-70 ||||$\overline{)||||}$ 5 70-80 |||| ∣∣$\overline{)||||}|$ 6 80-90 ||||$\overline{)||||}$ 5 90-100 |||$|||$ 3 Total N = 62 The cumulative frequency table of less than type for the given data is as follows: ​ Class (Marks obtained) Frequency (No. of students) Less than type cumulative frequency 0-10 4 4 10-20 3 7 20-30 8 15 30-40 9 24 40-50 13 37 50-60 6 43 60-70 5 48 70-80 6 54 80-90 5 59 90-100 3 62 Total N = 62 (i) The number of students who obtained less than 40 marks is 24. (ii) The number of students who obtained less than 10 marks is 4. (iii) The number of students who students who obtained less than 60 marks is 43. (iv) The cumulative frequency of the class 50-60 is 43.

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