1. OBJECTIVES:
During the period, the students are
expected to:
1. identify the different Measures of
Variability;
2. give the formula to compute each
Measure of Variability;
3. solve problems involving Measures of
Variability ( ungrouped data ).

2. Boys Girls
Frederick 70 Grace 82
Russel 95 Irish 80
Murphy 60 Abigail 83
Jerome 80 Sherry 81
Tom 100 Kristine 79
Mean: 81 Mean: 81
Scores of 5 Boys and 5 Girls in
Mathematics

3. Boys
60 70 80 90 100
Girls
60 70 80 90 100

4. Measures of
Variability or
Dispersion

5. RANGE:
The difference between the highest and the
lowest observation
R = H – L
Boys: R = 100 – 60
R = 40
Girls: R = 83 – 79
R = 4
Therefore the
girls are more
homogeneous
than the boys in
their math
ability

6. Mean Deviation:
The average of the summation of the
absolute deviation of each observation
from the mean.
MD = Σ Xi - X
n

7. BOYS Xi Xi – X
Frederick 70 11
Russel 95 14
Murphy 60 21
Jerome 80 1
Tom 100 19
Mean: 81 Σ = 405 Σ = 66
M.D = 66 / 5
= 13.2

8. GIRLS Xi Xi – X
Grace 82 1
Irish 80 1
Abigail 83 2
Sherry 81 0
Kristine 79 2
Mean: 81 Σ = 405 Σ = 6
M.D = 6 / 5
= 1.2

9. MD ( boys ) = 13.2
MD ( girls ) = 1.2
- based from the computed Mean
Deviation, the girls are more
homogeneous than the boys.

10. VARIANCE:
The average of the squared deviation
from the mean.
Population Variance
σ 2
= Σ ( Xi – X ) 2
n
Sample Variance
s 2
= Σ ( Xi – X ) 2
n - 1

11. BOYS Xi Xi – X ( Xi – X ) 2
Frederick 70 -11 121
Russel 95 14 196
Murphy 60 -21 441
Jerome 80 -1 1
Tom 100 19 361
Mean: 81 Σ = 405 Σ = 1,120
σ2
= 1,120 / 5 s2
= 1,120 / 4
= 224 = 280

12. GIRLS Xi Xi – X ( Xi – X ) 2
Grace 82 1 1
Irish 80 1 1
Abigail 83 2 4
Sherry 81 0 0
Kristine 79 2 4
Mean: 81 Σ = 405 Σ = 10
σ2
= 10 / 5 s2
= 10 / 4
= 2 = 2.5

13. BOYS
σ2
= 1,120 / 5 s2
= 1,120 / 4
= 224 = 280
GIRLS
σ2
= 10 / 5 s2
= 10 / 4
= 2 = 2.5
The values of
the Variance
also reveals that
the score of
boys are more
spread out than
that of the girls.

14. STANDARD DEVIATION:
The square root of the Variance
BOYS
σ 2
= 224 s 2
= 280
σ = 14.97 s = 16.73
GIRLS
σ 2
= 2 s 2
= 2.5
σ = 1.41 s = 1.58

15. Question:
Why do you think the
RANGE is considered an
unreliable Measure of
Variability?

16. Answer:
The RANGE is considered
unreliable because we will only
use two values, the highest and the
lowest which is not a complete
representation of all the
observations.

17. Think about this:
Why do we need to work
harmoniously with
everyone?

18. Recap:
 What are the different
Measures of Variability?
 How do we compute for each
measure?

19. SEATWORK:
Given the table below, compute for R,
MD, s, and s2
Xi l Xi – X l ( Xi – X ) 2
17
15
22
19
18
Σ = Σ = Σ =

20. Xi l Xi – X l ( Xi – X ) 2
17 1.2 1.44
15 3.2 10.24
22 3.8 14.44
19 0.8 0.64
18 0.2 0.04
Σ = 91 Σ = 9.2 Σ = 26.8

21. 1. Range = 7
2. MD = 1.84
3. s = 2.59
σ = 2.32
4. s 2
= 6.7
σ 2
= 5.36