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 ).

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

Boys

60 70 80 90 100

Girls

60 70 80 90 100

Measures of Variability or

Dispersion

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

Mean Deviation: The average of the summation of the

absolute deviation of each observation from the mean.

MD = Σ Xi - X

n

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

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

MD ( boys ) = 13.2

MD ( girls ) = 1.2

- based from the computed Mean Deviation, the girls are more homogeneous than the boys.

VARIANCE:The average of the squared deviation

from the mean.

Population Varianceσ 2 = Σ ( Xi – X ) 2

nSample Variance

s 2 = Σ ( Xi – X ) 2

n - 1

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

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

BOYSσ2 = 1,120 / 5 s2 = 1,120 / 4

= 224 = 280

GIRLSσ2 = 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.

STANDARD DEVIATION:The square root of the Variance

BOYSσ 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

Question:

Why do you think the

RANGE is considered an unreliable Measure of

Variability?

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.

Think about this:

Why do we need to work harmoniously with

everyone?

Recap: What are the different

Measures of Variability? How do we compute for each

measure?

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 =

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

1. Range = 7 2. MD = 1.843. s = 2.59 σ = 2.324. s 2 = 6.7 σ 2 = 5.36