measuring data

1. Measures of Variability
- Also called the measures of dispersion
- it describes the number of spread for a
data set

2. Measures of Variability
(Range ,Variance and Standard Deviation)
Range – the difference between the
highest score and the lowest score
Range= HS-LS
Gr 1
R=83-79
R=4
Gr 2
R=100-60
R=40
Group 1 Group 2
Student A 83 Student A 80
Student B 79 Student B 70
Student C 81 Student C 60
Student D 82 Student D 100
Student E 80 Student E 95

3. Measures of Variability
Variance-the the square
of the standard deviation
of a given data. It
reflects the degree of
spread in the data set
Population Variance Formula
Sample Variance Formula
  s2
= sample variance
 Σ = sum of…
 Χ = each value
 x
̄ = sample mean
n = number of values in the sample
 σ = populationstandard deviation
 ∑ =sum of…
 X = each value
 μ= population mean
N =numberofvalues in thepopulation

4. Measures of Variability
 Standard Deviation – is the measure
of how the numbers are spread out
 Procedures
 1. Compute the mean
 2. Determine the deviation or difference
between the individual scores to the mean of the
scores
 3. Calculate the square of each deviation and get
the sum of the squared deviation
 4. If the data is a population, divide the sum by
n, if the data is a sample, divide the sum by n-1
 5. Find the square root of the quotient in step 4.
 σ2
= population variance
 Σ = sum of…
 Χ = each value
 μ = population mean
Ν = number of values in the population
 s=samplestandarddeviation
 ∑=sumof…
 X=eachvalue
 x
̅ =samplemean
n=numberofvaluesinthesample

5. Measures of Variability
 Compute for the Variance and Standard Deviation
 Population Variance
Gr 1
1. Mean=83+79+81+82+80
5
Mean=405
5
Mean=81
Group 1 Group 2
Student A 83 Student A 80
Student B 79 Student B 70
Student C 81 Student C 60
Student D 82 Student D 100
Student E 80 Student E 95
Performance Grades of Students in
their Group Activity:

6. Measures of Variability
 Compute for the Variance and standard deviation
Population Variance Population Standard Deviation
σ2
= 10
5 σ = 1.41
σ2
= 2
Sample Variance Sample Standard Deviation
s2
= 10
5-1 s = 1.58
s2
=2.5
Group 1 X X
̅ X-X
̅ (X-X
̅ )2
Student
A
83 81 2 4
Student
B
79 81 2 4
Student
C
81 81 0 0
Student
D
82 81 1 1
Student
E
80 81 1 1
Mean =81
∑=405 ∑=10

7. Measures of Variability
 Compute for the Variance and standard deviation ( Group 1)
Population Variance Population Standard Deviation
σ2
= 10
5 σ = 1.41
σ2
= 2
Sample Variance Sample Standard Deviation
s2
= 10
5-1 s = 1.58
s2
=2.5
Group 1 X X
̅ X-X
̅ (X-X
̅ )2
Student
A
83 81 2 4
Student
B
79 81 2 4
Student
C
81 81 0 0
Student
D
82 81 1 1
Student
E
80 81 1 1
Mean =81
∑=405 ∑=10

8. Measures of Variability
 Compute for the Variance and standard deviation Population Variance Population
Standard Deviation
σ2
= 1,120
5σ = 14.97
σ2
= 224
Sample Variance Sample Standard Deviation
s2
= 1,120
5-1 s = 16.73
s2
=280
Group 2 X X
̅ X-X
̅ (X-X
̅ )2
Student
A
80 81 1 1
Student
B
70 81 11 121
Student
C
60 81 21 441
Student
D
100 81 19 361
Student
E
95 81 14 196
Mean =81
∑=405 ∑=1,12
0
Gr 2
1. Mean=80+70+60+100+95
5
Mean= 405
5
Mean=81

9. Comparison
Measures of Variability Group 1 Group 2
Mean 81 81
Range 4 40
Variance σ2
= 2 σ2
= 224
s2
=2.5 s2
=280
Standard Deviation σ = 1.41 σ = 14.97
s = 1.58 s = 16.73
Interpretation:
There is a consistency on the performance grades of group members in
Group 1 than Group 2
Students are more homogenous in their performance grade in Group 1 than
Group 2

10. Exercise
Compute for the Range, Variance , and
Standard Deviation of the following
sample population in their Statistics
subject:
19, 34, 20, 49, 23

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