Question 20 Case Study Based- 4
100m RACE
A stopwatch was used to
find the time that it took a
group of students to run 100 m.
(a) Estimate the mean time taken by a student to finish the race. (i) 54 (ii) 63 (iii) 43 (iv) 50
Mean(𝑥 ̅) = (∑▒𝒇𝒊𝒙𝒊)/(∑▒𝒇𝒊)
= 1720/40
= 43
Mean time is 43
(b) What wiil be the upper limit of the modal class ? (i) 20 (ii) 40 (iii) 60 (iv) 80 Modal class is class with highest frequency
∴ 40 − 60 is the modal class
And Upper limit = 60
(c) The construction of cummulative frequency table is useful in determining the (i) Mean (ii) Median (iii) Mode (iv) All of the aboveCummulative frequency table is used to find the Median
(d) The sum of lower limits of median class and modal class is (i) 60 (ii) 100 (iii) 80 (iv) 140 Modal class is class with highest frequency
∴ 40 − 60 is modal class
To find Median Class,
We find cummulative freqeuncy
𝑛/2=40/2 = 20
∴ 40 − 60 has cummulative frequency greater than 20
Thus, 40 − 60 is the Median Class
∴ Sum of Lower Limits of Median class and Modal class = 40 + 40 = 80
(e) How many students finished the race within 1 minute? (i) 18 (ii) 37 (iii) 31 (iv) 8
Students finished the race within 1 minute
= Students between 0 − 20
+ Students between 20 − 40
+ Students between 40 − 60
= 8 + 10 + 13
= 31

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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