By the end of this lesson, you should learn:
The concept was first introduced by
Karl Pearson in 1893.
It is the most useful and popular
measure of dispersion.
It is always calculated from arithmetic
mean, median and mode is not
considered.
It is the positive square root of the
average of squared deviation taken
from arithmetic mean
It is represented by Greek letter
(sigma) Σ or σ,
Formula:
It considers all the items of the series.
It is less affected by fluctuations of sampling.
It is the only measure of variation capable of algebraic
treatment.
The value of standard variation is based on every
observation in a set of data.
Compared to other measures of dispersion, calculation of
standard deviation are difficult.
While calculating standard deviation, more weight is given to
extreme values and less to those near to mean.
It cannot be calculated in open intervals.
If two or more data set were given in different units,
variation among those data set cannot be compared.
Σ (x
S=
-��ҧ)² ______
____ n -1
Find the mean.
Calculate the difference between each score and mean.
Square the difference between each score and the mean
Add up all the squares of the difference between each
score and the mean.
Divide the obtained sum by n-1.
Extract the positive square root of the quotient.
��ഥ
How to find the Mean ?
Add all your values and divide the sum to
the number of values.
210 / 6 = 35
73 - 35 = 38
11- 35 = -24
49 - 35 = 14
35 - 35 = 0
15 - 35 = -20
27 - 35 = -8
38² = 1444
-24² = 576
14² = 196
0² = 0
-20² = 400
-8² = 64
5
2680 S=
S = _______ 6 - 1 53
S = 2680
________
SD = 23.5
Find the standard deviation of the scores 21, 25, 22, 23 and 20.
Find the standard deviation of the scores 6, 7, 8, 9 and 10
S= Σ f (x
_________ - ��ҧ)²
n -1
Calculate the mean.
Get the deviation by finding the difference of each midpoint from
the mean.
Square the deviations and find its summation.
Substitute in the formula.
How to find the
MIDPOINT?
28 + 29 = 57
57 / 2 = 28.5
26 + 27 = 53
53 / 2 = 26.5
Multiply Frequency (f) to Midpoint 4 x
28.5 = 114
9 x 26.5 = 238.5
12 x 24.5 = 294
How
to get the Mean ��ഥ ? Get the summation
of your FMp column. Do the same for
Frequency (f) column.
��ഥ =
��ഥ = Σ 2014
f.mf 100
��ഥ = 20.14
Then, find the difference between your Mp and
��ഥ.
28.5 - 20.14 =8.36
26.5 - 20.14 = 6.36
24.5 - 20.14 = 4.36
Find the square of your answer in Mp - ��ഥ
column.
8.36² = 69.89
6.36² = 40.45
multiply frequency (f) to
your answer in ( Mp - ��ഥ )²
column.
4 x 69.89 = 279.56
And add everything in your
f(Mp- ��ഥ )² column.
S = 1747.08
________
Σ f (x -��ҧ)² 100 -1
S = __________ n -1 S = 1747.08
_________
99
SD = 4.20
17.65 S =
The following data represents the age
distribution of a sample of 100 people covered by health insurance
(private or government). The sample was taken from 2003.
Age Number
25 – 34 23
35 – 44 29
45 - 54 28
55 – 64 20
The following data represents the high
temperature distribution in degrees Fahrenheit for a sample of 40
days from the month of August in Chicago since 1872.
Temperatur Days
e 60 – 69 3
70 – 79 15
80 – 89 17
90 – 99 5
Σ f (x - ��)²
σ= S= __________
n
��ҧ)²
________
Σ f (x - n-1
