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Solution


Q.

A stopwatch was used to time a 100-metre race run by a group of students. The sports teacher carefully recorded their times in seconds, which are presented in the table below.

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 information, answer the following questions:

 

(iii) (a) Find the mean time taken by students to complete the race.
1 43  
2 44  
3 42  
4 41  

Ans.

(1)

We have,

Time No. of students (f?) Class Marks (x?) f?x?
0 – 20 8 10 80
20 – 40 10 30 300
40 – 60 13 50 650
60 – 80 6 70 420
80 – 100 3 90 270
Total Σf? = 40   Σf?x? = 1720

So, x¯=∑fixi∑fi=172040=43

∴The mean time taken by students to complete the race is 43 seconds.