Case-Study4 marksYear: 2024MediumCBSE Class 10
statisticsmodemedian-classcase-study
Question
Activities like running or cycling reduce stress and the risk of mental disorders like depression. Running helps build endurance. Children develop stronger bones and muscles and are less prone to gain weight. The physical education teacher of a school has decided to conduct an inter school running tournament in his school premises. The time taken by a group of students to run 100 m, was noted as follows:

| Time (in seconds) | 0−20 | 20−40 | 40−60 | 60−80 | 80−100 |
|---|---|---|---|---|---|
| Number of students | 8 | 10 | 13 | 6 | 3 |
Based on the above, answer the following questions:
(i) What is the median class of the above given data?
(ii) (b) Find the mode of the above given data.
(iii) How many students took time less than 60 seconds? Solution
1
(i) Total students =40. 2N=20. Cumulative frequencies: 8,18,31,37,40. Median class =40−60
+1 mark2
(ii)(b) Modal class =40−60 (f1=13, f0=10, f2=6, h=20)
+0.5 marks3
Mode =40+2×13−10−613−10×20=40+103×20=46
+1.5 marks4
(iii) Students who took time less than 60 seconds =8+10+13=31
+1 mark