Mathematics for Construction

8 Mathematics for Construction

TASK 2
Scenario 1
Revenue
(Class Interval)
Number of customers
(£1000)
January July
0 – 5 27 22
5 – 10 38 39
10 – 15 40 69
15 – 20 22 41
20 – 30 13 20
30 – 40 4 5
Solution
a) Histogram for each January and July distribution can be represented in following way –
Revenue
Number of
customers
in January (£1000)
0 to 5 27
5 to 10 38
10 to 15 40
15 to 20 22
20 to 30 13
30 to 40 4
1

Now, to calculate mode, firstly convert the unequal distribution into equal class interval in
following way –
Revenue
Number of
customers
(£1000)
January
0 to 10 65 (27 + 38)
10 to 20 62 (40 + 22)
20 to 30 13
30 to 40 4
From the above table, the highest frequency lies in the group of (0-10), therefore, taking this
class as modal class, mode of data can be calculated by using below formula
Mode (z) = L + f1 – f0 x h
2 f1 – f0 – f2
where, f1 gives highest frequency = 65
f0 lies above highest frequency = 0 and,
f2 lies below highest frequency = 62
2

h represents difference of class interval = 10 while,
L is the lower interval of modal class = 0,
Therefore, using these values, mode can be calculated as -
Mode (z) = 0 + 65 – 0 x 10
2 x 65 – 0 – 62
= 0 + 65 x 10
130 – 62
≈ 9.54
For July month -
Revenue
Number of
customers
in July (£1000)
0 to 5 22
5 to 10 39
10 to 15 69
15 to 20 41
20 to 30 20
30 to 40 5
3

Now, for calculating mode, data of July month also convert into equal distribution in following
manner –
Revenue
Number of
customers
in July (£1000)
0 to 10 61 (22 + 39)
10 to 20 110 (69 + 41)
20 to 30 20
30 to 40 5
4