Question

CASE STUDY BASED:
For a 100 M RACE a stopwatch was used to find the time that it took a group of students to run 100m.
Tim in sec No of students
0-20 8
20-40 10
40-60 13
60-80 6
80-100 3​

Answer 1

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 :  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

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

40-60  is modal class  hence upper limit of modal class = 60

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

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