Mathematics for Construction

8 Mathematics for
Construction

Table of Contents
TASK 2 ...........................................................................................................................................3
Scenario 1.....................................................................................................................................3
Scenario 2.....................................................................................................................................6
TASK 3..........................................................................................................................................12
Scenario 1...................................................................................................................................12
Scenario 2...................................................................................................................................16
TASK 4..........................................................................................................................................18
Scenario 1...................................................................................................................................18
Scenario 2 ..................................................................................................................................20
Scenario 3...................................................................................................................................22

TASK 2
Scenario 1
A.) Histogram and determining mode of each rectangle distribution
Solution
Revenue Class width January Height of rectangle in histogram
0 -4 5 27 5 14.5
5 to 9 5 38 5
10 to 14 5 40 5
15 to 19 5 22 5 h1 = 6.5-5 = 1.5
20 to 29 2* standard 13 6.5
30 to 39 2* standard 4 2 h2 = 6.5 - 2 4.5
Lower limit of modal class is = 20
Mode = L + h1 * [w/ (h1 + h2)]
L = 20 h1 = 1.5 h2 = 4.5 w = 10
On substituting values we have
mode = 22.5 (for January month )

Similarly for July month we have:
Revenue Class width July Height of rectangle in histogram
0 -4 5 22 5
5 to 9 5 39 5
10 to 14 5 69 5
15 to 19 5 41 5 h1 = 10-5 = 5
20 to 29 2* standard 20 10
30 to 39 2* standard 5 2.5 H2 = 10-2.5 =
7.5
Lower limit of modal class = 20
L = 20 h1 = 5 h2= 7.5 w= 10
mode = 20+ 5*[10/(5+7.5)]
mode = 24 (For July month )
B.) Cumulative frequency distribution curve

Solution
January Cumulative frequency
27 5
38 10
40 15
22 20
13 26.5
4 28.5
Quartile 24.5 Median
15.25 Q1
24.5 Q2
35.25 Q3
Interquartile 20 Q3 -Q1
Similarly for July month:

July Cumulative frequency
22 5
39 10
69 15
41 20
20 30
5 32.5
Quartile 30.5 Median
20.5 Q1
30.5 Q2
40.5 Q3
Interquartile 20 Q3 -Q1
C.) Mean, range and standard deviation
Solution
Mean Range Standard deviation