The document discusses measures of position such as quartiles, percentiles, and deciles. It provides examples of how to calculate these measures from sets of data and determines an individual's performance relative to these measures. Key points include: - Quartiles divide a distribution into 4 equal parts, percentiles divide into 100 equal parts, and deciles divide into 10 equal parts. - The median is the middle number in a data set and is equal to the 2nd quartile. - Examples are provided for calculating the lower quartile (Q1), middle quartile (Q2), and upper quartile (Q3) using both the Mendenhall and Sincich method as well as linear interpolation. -

1. WHAT I KNOW

2. If you wish to divide a class into 10
equal parts, which measure of
position is appropriate to use?
A. decile C. median
B. percentile D. quartile

3. When a distribution is divided into 4
equal parts, each score point that
describes a distribution is called a
_________.
A. decile C. median
B. percentile D. quartile

4. Which of the following is in
equal position with the median
score?
A. 1st quartile C. 3rd quartile
B. 5th decile D. 90th percentile

5. When a distribution is divided into
100 equal parts, each score point that
describes a distribution is called a
_________.
A. decile C. median
B. percentile D. quartile

6. In a 50-item Statistics Test, Anna
obtained a score of 42 which is
considered as the 8th decile. Which one
from the following statements is NOT
TRUE?
A. Anna scored equal or above 80% of her classmates.
B. Anna’s score is below the 3rd quartile.
C. Twenty percent (20%) of her classmates scored higher or equal
to 42.
D. If the passing mark is the 50th percentile, then she passed the
test.

7. Which of the following is equal
to the 7th decile in terms of
position?
A. Q3 C. P70
B. P75 D. D5

8. If Q1 = 15 and Q3 = 23, then
the interquartile range is ____.
A. 7 C. 8
B. 9 D. 10

9. Which of the following is less
than the 70th percentile in
terms of position?
A. Median C. 8th decile
B. 7th decile D. Upper Quartile

10. If there are 10 numbers in a
set of data, the 2nd quartile is
the _________.
A. 3rd number
B. 4th number
C. 5th number
D. average of 5th and 6th number

11. If the passing score of a 100-item
standardized test is 50 and
considered as the 60th percentile,
which one from the following
statements is NOT TRUE?
A. 60% of the examiners got a score lower than or equal to 50.
B. 40% of the examiners garnered a score of 50 and above.
C. Obtaining a score that is in the 5th decile means passing the test.
D. 40% of the examiners answered 50 or more questions correctly.

12. CALCULATING
MEASURES OF POSITION

13. WHAT’S IN
1. Quartiles are the score points
which divide a distribution into
equal parts.
A. two
B. four
C. ten
D. hundred

14. WHAT’S IN
2. The median is also the _________.
A. 1st quartile
B. 2nd quartile
C. 3rd decile
D. 75th percentile

15. WHAT’S IN
3. Which of the following statement is
incorrect?
i. D4 is also equal to P40
ii. 75% of the data has a value of < Q3
iii. Percentiles are ninety-nine points
which divides a distribution into one
hundred equal parts
A. I B. ii C. iii D. none

16. WHAT’S IN
4. Given the scores of test in Mathematics
: 3, 3, 4, 5, 7, 7, 11, 14, 14, 15. What are
the scores less than or equal to 25% of the
data ?
A. 3, 3, 4
B. 4, 5, 7
C. 5,7,7
D. 14, 14, 15

17. WHAT’S IN
5. The upper quartile is equal to _____
.
A. Q1
B. Q2
C. Q3
D. D9

18. WHAT’S NEW
Eleven students taking a modular learning
have the scores in their English test as
follows : 23 , 11, 28 , 15, 19, 10, 17, 3, 25,
26 and 21.
How can they determine their position in a
given set of data ?

19. First, arrange the set of scores in ascending order
How the lower quartile (Q1),middle quartile (Q2), and
the upper quartile (Q3) of the scores are obtained?
WHAT’S NEW

20. WHAT’S IT
Quartile for Ungrouped Data
Using Mendenhall and Sincich Method
Using Linear Interpolation

21. USING MENDENHALL AND SINCICH
METHOD
Example:
Given the set of data 32, 34, 18, 19, 24 , 27,
30, 12, 13. Find the lower and the upper
quartile of the data

22. USING LINEAR INTERPOLATION
Example:
Given the set of scores of 13 students in
their Math quiz, find the first quartile (Q1)
and the 3rd quartile (Q3) using linear
interpolation
33,11, 7,31,15,18,20,14,21,23,19,27,36