This document discusses measures of position in descriptive statistics, including quartiles, deciles, percentiles, and percentile ranks. It provides examples of calculating these measures from data sets and interpreting what they represent. Quartiles divide a data set into four equal parts, with the lower quartile being the middle number between the lowest number and median. The median is the middle number. Deciles and percentiles similarly divide data into 10 or 100 equal parts. Percentile rank indicates the percentage of values below a particular data point.

1. ADVANCED
STATISTICS
MICHAEL JAMES E. ERGINO
Subject Teacher

2. CHAPTER 2
DESCRIPTIVE
STATISTICS

3. LESSON 11
MEASURES OF
POSITION

4. LESSON 11 - MEASURES OF POSITION
WHAT IS MEASURE OF POSITION?
MEASURES OF POSITION give us a way to see where a certain data point or
value falls in a sample or distribution.
• A measure can tell us whether a value is about the average, or whether it’s
unusually high or low.
• Measures of position are used for quantitative data that falls on some numerical
scale. Sometimes, measures can be applied to ordinal variables - those
variables that have an order, like first, second…fiftieth.
Common Measures of Position
1. Quartile
2. Decile
3. Percentile
4. Percentile rank

5. LESSON 11 - MEASURES OF POSITION

6. LESSON 11 - MEASURES OF POSITION

7. LESSON 11 - MEASURES OF POSITION

8. LESSON 11 - MEASURES OF POSITION
FIND THE QUARTILES OF THE 1ST QUARTER GRADES
OF 9 STUDENTS IN STATISTICS, GIVEN THE DATA SET:
81, 84, 88, 90, 87, 94, 96, 85, 97
► 81, 84, 85, 87, 88, 90, 94, 96, 97 n = 9
= 0.25 (9 +1)
= 0.25 (10)
= 2.5 (round up)
= 3
The lower quartile is
the 3rd data which is
85.
= 0.5 (9 +1)
= 0.5 (10)
= 5
The median is the 5th
data which is 88.
= 0.75 (9 +1)
= 0.75 (10)
= 7.5 (round down)
= 7
The upper quartile is
the 7th data which is
94.

9. LESSON 11 - MEASURES OF POSITION

10. LESSON 11 - MEASURES OF POSITION

11. LESSON 11 - MEASURES OF POSITION
A GROUP OF STUDENTS OBTAINED THE FOLLOWING SCORE
IN THEIR 50-ITEM TEST:
24, 25, 27, 28, 31, 32, 34, 37, 38, 41, 43, 47 ► n = 12
= 0.25 (12 + 1)
= 0.25 (13)
= 3.25th position
► 28 – 27 = 1
► 1 (0.25) = 0.25
► 27 + 0.25 = 27.25
Thus, the lower quartile is 27.25.
= 0.75 (12 + 1)
= 0.75 (13)
= 9.75th position
► 41 – 38 = 3
► 3 (0.75) = 2.25
► 38 + 2.25 = 40.25
Thus, the upper quartile is 40.25.

12. LESSON 11 - MEASURES OF POSITION

13. LESSON 11 - MEASURES OF POSITION

14. LESSON 11 - MEASURES OF POSITION
THE GRADE 9 ADVISER COLLECTS DATA ON THE
NUMBER OF HOURS SLEEP OF GRADE 9 DILIGENCE
STUDENTS IN PCLU AND GOT THE DATE SET:
5, 5, 6, 6, 6, 7, 8, 8, 9, 9, 10. Find 𝐷3, 𝐷6, 𝑎𝑛𝑑 𝐷9.
𝐷3 =
𝑘
10
(𝑛 + 1) 𝐷6 =
𝑘
10
(𝑛 + 1) 𝐷9 =
𝑘
10
(𝑛 + 1)
𝐷3 =
3
10
(11 + 1)
𝐷3 =
3
10
(12)
𝐷3 = 3.6 ≈ 4
𝑫𝟑 = 𝟔
𝐷6 =
6
10
(11 + 1)
𝐷6 = 7.2 ≈ 7
𝐷6 =
6
10
(12)
𝑫𝟔 = 𝟖
𝐷9 =
9
10
(11 + 1)
𝐷9 =
9
10
(12)
𝐷9 = 10.8 ≈ 11
𝑫𝟗 = 𝟏𝟎

15. LESSON 11 - MEASURES OF POSITION

16. LESSON 11 - MEASURES OF POSITION

17. LESSON 11 - MEASURES OF POSITION

18. LESSON 11 - MEASURES OF POSITION

19. LESSON 11 - MEASURES OF POSITION

20. LESSON 11 - MEASURES OF POSITION
FIND THE PERCENTILE RANK OF A TEST SCORE OF
92 IN THE DATE SET: 83, 94, 91, 90, 88, 85, 89, 92, 84,
95, 97, 82, 99.
► 82, 83, 84, 85, 88, 89, 90, 91, 92, 94, 95, 97, 99 n=13
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒 𝑟𝑎𝑛𝑘 𝑜𝑓 𝑥 =
(𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑎𝑙𝑢𝑒𝑠 𝑏𝑒𝑙𝑜𝑤 𝑥) + 0.5
𝑛
𝑥100
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒 𝑟𝑎𝑛𝑘 𝑜𝑓 92 =
8 + 0.5
13
𝑥100
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒 𝑟𝑎𝑛𝑘 𝑜𝑓 92 =
8.5
13
𝑥100
𝑷𝒆𝒓𝒄𝒆𝒏𝒕𝒊𝒍𝒆 𝒓𝒂𝒏𝒌 𝒐𝒇 𝟗𝟐 = 𝟔𝟓. 𝟑𝟖𝟒𝟔%

21. LESSON 11 - MEASURES OF POSITION
FIND THE PERCENTILE RANK OF A TEST SCORE OF
97 IN THE DATE SET: 83, 94, 91, 90, 88, 85, 89, 92, 84,
95, 97, 82, 99.
► 82, 83, 84, 85, 88, 89, 90, 91, 92, 94, 95, 97, 99 n=13
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒 𝑟𝑎𝑛𝑘 𝑜𝑓 𝑥 =
(𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑎𝑙𝑢𝑒𝑠 𝑏𝑒𝑙𝑜𝑤 𝑥) + 0.5
𝑛
𝑥100
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒 𝑟𝑎𝑛𝑘 𝑜𝑓 97 =
11 + 0.5
13
𝑥100
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒 𝑟𝑎𝑛𝑘 𝑜𝑓 97 =
11.5
13
𝑥100
𝑷𝒆𝒓𝒄𝒆𝒏𝒕𝒊𝒍𝒆 𝒓𝒂𝒏𝒌 𝒐𝒇 𝟗𝟕 = 𝟖𝟖. 𝟒𝟔𝟏𝟓%

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