Mathematics for Construction

8 Mathematics for Construction

TASK 2
Scenario 1
Revenue Number of customers
(£1000)
January July
Less than 5 27 22
5 and less than 10 38 39
10 and less than 15 40 69
15 and less than 20 22 41
20 and less than 30 13 20
30 and less than 40 4 5
Firstly, organised the above table into grouped frequency in following manner -
Revenue Number of customers
(£1000)
January July
0 to 5 27 22
5 to 10 38 39
10 to 15 40 69
15 to 20 22 41
20 to 30 13 20
30 to 40 4 5
1

Since, this table is not in regular interval of group, so convert it into equal grouped intervals by
combining first two rows then, second two rows as 0 – 10 and 10 – 20, so that all group ranges
from 10 in following way -
Equal class interval -
Revenue
Number of customers
(£1000)
January July
0 to 10 65 61
10 to 20 62 110
20 to 30 13 20
30 to 40 4 5
Now, to construct histogram of each and find other central tendencies, separate above table into
two categories, firstly for January and secondly to July -
Revenue
Number of customers
(£1000)
January
0 to 10 65
10 to 20 62
20 to 30 13
30 to 40 4
Revenue Number of customers
2

(£1000)
July
0 to 10 61
10 to 20 110
20 to 30 20
30 to 40 5
a) Histogram of January month -
Now, mode can be calculated by using following formula -
Mode (z) = l + f1 – f0 x h
2 f1 – f0 - f2
here, f1 refers highest frequency, which is 65 as per above table
f0 refers to previous frequency from maximum, which is 0 and,
3
0 to 10
10 to 20
20 to 30
30 to 40
0 10 20 30 40 50 60 70
Number of customers (£1000)
January

f2 is the next frequency, i.e. 62
h is the class difference = 10 and,
l is the lower-bound interval of mode class = 0,
so, mode can be calculated as -
Mode (z) = 0 + 65 – 0 x 10
2 x 65 – 0 – 62
= 0 + 65 x 10
130 – 62
= 0 + 650 / 68
= 9.55
a) Histogram of July month -
From this histogram, 10 to 20 group has highest frequency, so, taking this group as modal
class of grouped frequency, then mode can be calculated in following way –
Mode (z) = l + f1 – f0 x h
2 f1 – f0 - f2
4
0 to 10
10 to 20
20 to 30
30 to 40
0 20 40 60 80 100 120
Number of customers (£1000)
July