Question

Chapter 1: Representation of data
5 Each of the 70 trainees at a secretarial college was asked to type a copy of a particular document. The times
taken are shown, correct to the nearest 0.1 minutes, in the following table.
Time taken (min)
2.6-2.8
2.9-3.0
3.1-3.2
3.3-37
No, trainees (f)
15
25
a Explain why the interval for the first class has a width of 0.3 minutes.
b Represent the times taken in a histogram.
c Estimate, to the nearest second, the upper boundary of the times taken by the fastest 10 typists.
d It is given that 15 trainees took between 3.15 and b minutes. Calculate an estimate for the value of 6 when:
i b> 3.15
ii b< 3.15.
20
10
6 A railway line monitored 15% of its August train journeys to find their departure delay times. The results are
shown below. It is given that 24 of these journeys were delayed by less than 2 minutes

Answer 1

Answer:

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Answer 2

Given :   70 trainees at a secretarial college was asked to type a copy of a particular document.

The times taken are shown, correct to the nearest 0.1 minutes

Time taken (min)      No, trainees (f)

2.6-2.8                        15

2.9-3.0                        25

3.1-3.2                         20

3.3-37                          10

To Find :Explain why the interval for the first class has a width of 0.3 minutes.

Represent the times taken in a histogram.

Estimate, to the nearest second, the upper boundary of the times taken by the fastest 10 typists.

Solution:

Class width   = Lower limit of next class - lower limit of that class

= 2.9 - 2.6

= 0.3

or Class width = upper boundary - lower boundary

= 2.85  - 2.55

= 0.3

Time taken (min)      No, trainees (f)

2.55 - 2.85                        15

2.85 - 3.05                         25

3.05 - 3.25                         20

3.25 -3.75                           10

upper boundary of the times taken by the fastest 10 typists.

2.55  + (10/15) * 0.3

= 2.75

= 2.8 secs

from the histogram :

b> 3.15

b = 3.55

b < 3.15

b = 3.01

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