18. A stopwatch was used to find the time that it took a group of students to run 100 m.
0-20
20-40
40-60
60-80
80-100
Time(in
sec)
No.Of
students
oo
10
13
6
3
1. Estimate the mean time taken by a student to finish the race.
(i)54 (ii)63 (iii)43 (iv)50
2. What wiil be the upper limit of the modal class ?
(i)20 (ii)40 (iii) 60 (iv)80
3. The sum of lower limits of median class and modal class is
(1)60 (ii) 100 (iii) 80 (iv)140
4. How many students finished the race within 1 minute?
(i) 18 (ii)37 (iii)31 (iv)8
Answers
Answer:
1. (D) 50
2.(A)20
3.(A)60
4. it should be 13
Given : A stopwatch was used to find the time that it took a group of students to run 100 m.
Time (in sec) 0-20 20-40 40-60 60-80 80-100
No. of students 8 10 13 6 3
To Find : 1. Estimate the mean time taken by a student to finish the race.
(i)54 (ii)63 (iii)43 (iv)50
2. What wiil be the upper limit of the modal class ?
(i)20 (ii)40 (iii) 60 (iv)80
3. The sum of lower limits of median class and modal class is
(1)60 (ii) 100 (iii) 80 (iv)140
4. How many students finished the race within 1 minute?
(i) 18 (ii)37 (iii)31 (iv)8
Solution:
Time (in sec) f cf
0-20 8 8
20-40 10 18
40-60 13 31
60-80 6 37
80-100 3 40
1 minute = 60 sec
Time less than 60 sec = 31 Students
31 students finished the race within 1 minute
option iii) is correct
mean time taken by a student to finish the race = (10*8 + 30*10+50*13+70*6+90*3)/40
= (8 + 30 + 65 + 42 + 27)/4
= 172/4
= 43 secs
option iii) is correct
40-60 is modal class hence upper limit of modal class = 60
option iii) is correct
The construction of cumulative frequency table is useful in determining the Median
Modal class and median class = 40 - 60
The sum of lower limits of median class and modal class is
40 + 40 = 80
option iii) is correct
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