Question

The length of time taken by 80 drivers to complete a journey is given in the table below:
Times (in minutes) 70-80 80-90 90-100 100-110 110-120 120-130
Number of drivers
4
10
14
20
24
8
(i)
What is the estinate of the mean time taken to complete the journey ?
(a) 104.25 minute
(b) 94 minute
(c) 101.5 minute
(d) 112 minute​

Answer 1

The estimated mean time taken to complete the journey is (a) 104.25 minutes.

Given:-

Refer to the image attached below

To find:-

The mean of the time taken to complete the journey

Solution:-

Firstly we need to find the midpoint (m) of each class interval. The formula for finding the midpoint is;

$Midpoint=\frac{Upper point+lower point}{2}$

Once you find the midpoint for each class interval you need to multiply the midpoint by the frequency of the respective class interval.

We then need to find the sum of frequency (f) and the sum of (f.m)

To find the mean we use the formula:

Mean = ∑fm/∑f

Mean = 8340/80

Mean = 104.25

∴The estimated mean time taken to complete the journey is 104.25 minutes.

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