1. Introduction to Statistics for Built
Environment
Course Code: AED 1222
Compiled by
DEPARTMENT OF ARCHITECTURE AND ENVIRONMENTAL DESIGN (AED)
CENTRE FOR FOUNDATION STUDIES (CFS)
INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA

2. Lecture 9
Measures of variability/dispersion
Part II
Today’s Lecture:
 The average absolute deviation
 The Standard deviation

3. What is ‘deviation’?
English Dictionary: ‘Departure from a standard or
norm’.
In Statistics, deviation is defined as the difference
between one of a set of values and some fixed
value, usually the mean of the set.
The difference between each data item and the
mean of all the data items in a data set is called a
deviation.

4. The average deviation
The average deviation is one of several measures of variability
that statisticians use to characterize the dispersion among
the measures in a given population/sample.
To calculate the average deviation of a set of scores it is first
necessary to compute their mean, and then specify the
distance between each score and that mean without
regard to whether the score is above or below the mean.
The average deviation is then defined as the mean of these
absolute values.

5. Calculating Average Deviation
1. Find the average of your measurements.
2. Find the difference between the average and
each of your measurements use absolute
value.
3. Find the average of these differences. This
will be your deviation.

6. Exercise 1
The data set below indicates the age of trucks.
Calculate the average (mean) absolute
deviation for the data set.
18, 19, 19, 19, 19, 19, 20, 20, 45, 45, 46, 47, 48,
50.

7. The average absolute deviation
• The mean/average absolute deviation: is the
absolute deviation from the mean.
• The average absolute deviation from the
median: is the absolute deviation from the
median.
• The average absolute deviation from the mode:
is the absolute deviation from the mode.

8. Measure of central
tendency
Absolute deviation
Mean = 5
Median = 3
Mode = 2
The absolute deviation cont.

9. The standard deviation
The standard deviation is the most important & most
useful measure of spread.
Standard deviation = the positive square root of the
average of the squared deviations of the individual
data items about their mean.
Standard deviation = (how far away items in a data set
are from their mean).
The most widely used for describing the spread of a
group of scores.
Calculating standard deviation

10. Calculating std. deviation
Ages (x) Mean age (x) (x – x) (x – x)²
18 31 -13 169
19 31 -12 144
19 31 -12 144
19 31 -12 144
19 31 -12 144
19 31 -12 144
20 31 -11 121
20 31 -11 121
45 31 14 196
45 31 14 196
46 31 15 225
47 31 16 256
48 31 17 289
50 31 19 361
10
434 2654
x 434
14
= = 31Mean,
Std. deviation, s =
√
√ 2654
14 - 1
Total
√ 204.15
14.29
All deviations are squared
to eliminate negative
values
Assuming the data
is a sample

11. Class
Boundary
(f) (m) f.m f.m²
18 – 23 2 20 40 800
23 – 28 3 25 75 1875
28 – 33 3 30 90 2700
33 – 38 5 35 175 6125
38 – 43 9 40 360 14400
43 – 48 12 45 540 24300
48 – 53 20 50 1000 50000
53 – 58 21 55 1155 63525
58 – 63 28 60 1680 100800
63 – 68 22 65 1430 92950
68 – 73 7 70 490 34300
73 – 78 9 75 675 50625
78 – 83 4 80 320 25600
83 - 88 5 85 425 36125
150Total 8455 504125
150(504125) - 8455²
150(150-1)
4136725
22350
185.09
=
=
=
s = 13.6

12. Exercise
Questions:
1. Which group did generally better in the exam?
2. Which group had the single lowest score?
3. Which group had the widest spread of scores?
4. Which group had the most homogenous scores on the test?
CENTRAL TENDENCY DISPERSION
Group Mean Mode Median Min. Max. Range SD
A 70 67 70 40 90 50 14
B 60 55 62 55 68 13 2