This document discusses measures of variability and quartile deviation. It defines quantiles as values that divide a data set into equal parts, including the median, quartiles, deciles, and percentiles. Quartiles (Q1, Q2, Q3) divide the data into four equal parts. The interquartile range is the difference between Q3 and Q1. The quartile deviation is half the interquartile range, or (Q3 - Q1)/2. The document provides steps for calculating quartiles and quartile deviation from both ungrouped and grouped data sets. An example calculation is shown for grouped test score data.

1. Lucy Sarah Blaisse Flores-Anas
Discussant
EDUCATION 309 – STATISTICS FOR
EDUCATIONAL RESEARCH
TOPIC: MEASURES OF VARIABILITY -
QUARTILE DEVIATION

2. • Quantiles are the extensions of the median
concept because they are values which divide a
set of data into equal parts.
a. Median – divides the distribution into two
equal parts.
b. Quartile – divides the distribution into four
equal parts.
c. Decile – divides the distribution into ten equal
parts.
d. Percentile – divides the distribution into one
hundred equal parts.

3. Quartiles are values in a given set of distribution
that divide the data into four equal parts. Each set
of scores has three quartiles. These values can be
denoted by Q1, Q2 and Q3.
 First quartile - Q1 (lower quartile) – The middle
number between the smallest number and the
median of the data set (25th Percentile).
 Second quartile - Q2 – The median of the data
that separates the lower and upper quartile
(50th Percentile).
 Third quartile - Q3 – (upper quartile)
The middle value between the
and the highest value of the
data set (75th Percentile).

4. • The difference between the upper
and lower quartiles is called the
Interquartile range. (IQR = Q3-Q1)
• Quartile deviation or Semi-
interquartile range is one-half the
difference between the first and
the third quartiles. (QD = Q3-Q1/2)

5. GETTING THE QUARTILE DEVIATION
FROM UNGROUPED DATA
• In getting the quartile deviation from ungrouped data,
the following steps are used in getting the quartiles:
• Arrange the test scores from highest to lowest.
• Assign serial numbers to each score. The first serial
number is assigned to the lowest test score, while the last
serial number is assigned to the highest test score.
• Determine the first quartile (Q1). To be able to locate Q1,
divide N by 4. Use the obtained value in locating the
serial number of the score that falls under Q1.
• Determine the third quartile (Q3), by dividing 3N by 4.
Locate the serial number corresponding to the obtained
answer. Opposite this number is the test score
corresponding to Q3.
• Subtract Q1 from Q3 and divide the difference by 2.

6. Score
Serial
Number
17
17
26
27
30
30
31
37
N = 8
1
2
3
4
5
6
7
8
Consider the test Scores table below:
𝑁
4
=
8
4
= 2
Q1 = (
17+ 26
2
)
= 21.5
QD = (
𝑄3−𝑄1
2
)
= (
30.5−21.5
2
)
= 4.5
3𝑁
4
=
3(8)
4
= 6
Q3 = (
30+31
2
)
= 30.5

7. GETTING THE QUARTILE DEVIATION
FROM GROUPED DATA
1. Cumulate the frequencies from the bottom to
the top of the grouped frequency distribution.
2. For the first quartile, use the formula
L = exact lower limit if the Q1 class
N/4 = locator of the Q1 class
N = total number of scores
CF = cumulative frequency below
the Q1 class
i = class size/interval
where:
Q1 =L +
𝑵
𝟒
− 𝑪𝑭
𝒇
(i)

8. 3. For the third quartile, use the formula
Q3 = L +
𝟑𝑵
𝟒
− 𝑪𝑭
𝒇
(i)
L = exact lower limit if the Q3 class
3N/4 = locator of the Q3 class
N = total number of scores
CF = cumulative frequency below the Q3 class
i = class size/interval
where:

9. COMPUTATION OF THE QUARTILE
DEVIATION FOR GROUPED TEST SCORES
Classes
Frequency
(f)
Cumulative
Frequency (CF)
46-50
41-45
36-40
31-35
26-30
21-25
16-20
11-15
5
7
9
10
8
6
4
4
N = 53
53
48
41
32
33
14
8
4

10. 𝑵
𝟒
=
𝟓𝟑
𝟒
= 13. 25
CF = 8 f = 6 L = 20.5
Q1 = L +
𝑵
𝟒
− 𝑪𝑭
𝒇
(i)
= 20. 5 +
𝟏𝟑.𝟐𝟓− 𝟖
𝟔
(5)
= 20. 5 +
𝟓.𝟐𝟓
𝟔
(5)
= 20. 5 +
𝟑𝟏.𝟓
𝟔
= 25.75
The computational procedures for determining the quartile
deviation for grouped test scores are reflected in the above table.
For the first quartile
𝟑𝑵
𝟒
=
𝟑(𝟓𝟑)
𝟒
= 40.5
CF = 32 f = 9 L = 35.5
Q3 = L +
𝟑𝑵
𝟒
− 𝑪𝑭
𝒇
(i)
= 35.5 +
𝟒𝟎.𝟓 − 𝟑𝟐
𝟓
(5)
= 35.5 +
𝟖.𝟓
𝟓
(5)
= 35.5 +
𝟒𝟐.𝟓
𝟔
= 40.22
For the third quartile

11. Thus QD = (
𝑸𝟑−𝑸𝟏
𝟐
)
After obtaining the first and third quartiles, we
can now compute QD.
QD = (
𝟒𝟎.𝟐𝟐−𝟐𝟓.𝟕𝟓
𝟐
)
= (
𝟏𝟒.𝟒𝟕
𝟐
)
= 7.235 or 7.24

12. Thank you and God Bless us all!