This document discusses measures of position and calculating quartiles from ungrouped data. It defines measures of position, ungrouped data, and quartiles. Quartiles (Q1, Q2, Q3) divide a data set into four equal parts. The document illustrates how to find the first, second, and third quartiles using the Mendenhall and Sincich method. It includes an example of finding the quartiles from a set of test scores. Activities, quizzes, and assignments are provided to reinforce calculating quartiles from ungrouped data.

1. Mathematics
Mathematics is not about numbers,
equations, computations, or algorithms: it
is about understanding.
— William Paul Thurston, American
mathematician
ELAM JETHER A. TABILOG
TEACHER

2. REVIEW (Answer)
Conditional
Probability
Conditional probability is
the measure of an event
given that another event
has already occurred.

3. Let’s Play it!

4. VERY GOOD!

5. GOOD JOB!

6. EXCELLENT!

7. Measures of Positions
• Measures of Positions have two types of data - the Ungrouped Data
and Grouped Data.
Measures of Position of Quartiles for Ungrouped
Data

8. OBJECTIVE
In this topic you are expected to;
a. illustrate the quartile for ungrouped data;
b. calculate the first quartile(Q1), second quartile (Q2) and third
quartile (Q3) in a given set of ungrouped data; and
c. appreciate the values of patience and perseverance in developing the
skill.

9. Definition: Measures Of Position
• Measures of Position tell where a specific data value falls
within the data set or its relative position in comparison with
other data values.
• The most common measures of position are quartiles, deciles
and percentiles.

11. Definition: Ungrouped Data
• Ungrouped Data are those data which are not
yet organized or arranged into frequency
distribution.

12. Definition: Quartiles
Quartiles – The score points which divide a distribution into four
equal parts. Twenty-five percent (25%) of the distribution are
below the first quartile, fifty percent (50%) are below the second
quartile, and seventy-five percent (75%) are below the third
quartile.

13. Illustration: Quartiles
a. 25% of the data has a value ≤ Q1
b. 50 % of the data has a value ≤ median or Q2
c. 75% of the data has a
value ≤ Q3

14. Illustration: Quartiles
• Q1, Q2 and Q3 are the quartile mark.
• Q1 is called the lower quartile or the first quartile and
Q3 is the upper quartile or the third quartile and
Q1<Q2<Q3, where Q2 is nothing but the median. It
means that it’s just only the middle.

15. How to find the Median?
If the number of items is odd, we can get the
median or Q2 by finding only the middle
value and if the number of items in the
distribution is even then we just simply get
the average of the two middle values
Example:
Number of
items:
Middle:
1,4,5
3
Odd
4
1,3,4,5
4
Even
3 + 4 =
7/ 2 = 3.5

16. Mendenhall and Sincich Method
• It is a method of finding the quartile value of a given set of data.
Lower Quartile(L)= Position of Q1 = 1/4(n+1), where n represents the total number of elements or terms.
 If L falls halfway between two integers, round it up. The Lth element is the lower quartile value (Q1).
Upper Quartile(U)= Position of Q3= 3/4(n+1), where n again represents the total number of elements or
terms.
 If U falls halfway between two integers, round it down. The Uth element is the upper quartile value
(Q3).

17. Example no. 1:
A group of students obtained the following scores in their statistics
quiz:
2, 5, 4, 8, 4, 7, 1, 5, 6
Find the Q1, Q2 and Q3.

18. Lower Quartile or Q1:
Step no. 1: Arrange the scores in ascending order.
1, 2, 4, 4, 5, 5, 6, 7, 8
Step no. 2: Find the value of n.
n= 9
Step no. 3: Write the formula.
Position of Q1 =
1
4
(n+1)
Step no. 4: Substitute the value of n in the formula.
Position of Q1 =
1
4
(9+1)

19. Step no. 5: Simplify
Position of Q1 =
1
4
(10)
Position of Q1 =
10
4
Position of Q1 =2.5
Step no. 6: Round it up.
Position of Q1 =2.5 = 3
Step no. 7: Locate the position of Q1 in the set of data.
1, 2, 4, 4, 5, 5, 6, 7, 8
The 3rd value is 4 so Q1 = 4

20. Upper Quartile or Q3:
Step no. 1: Arrange the scores in ascending order.
1, 2, 4, 4, 5, 5, 6, 7, 8
Step no. 2: Find the value of n.
n= 9
Step no. 3: Write the formula.
Position of Q3 =
3
4
(n+1)
Step no. 4: Substitute the value of n in the formula.
Position of Q3 =
3
4
(9+1)

21. Step no. 5: Simplify
Position of Q3=
3
4
(10)
Position of Q3=
30
4
Position of Q3=7.5
Step no. 6: Round it down.
Position of Q3 =7.5 = 7
Step no. 7: Locate the position of Q3 in the set of data.
1, 2, 4, 4, 5, 5, 6, 7, 8
The 7th value is 6 so Q3 = 6

22. Median or Q2:
Step no. 1: Arrange the scores in ascending order.
1, 2, 4, 4, 5, 5, 6, 7, 8
Step no. 2: Find the value of n.
n= 9
Step no. 3: Write the formula.
Position of Q2 =
1
2
(n+1)
Step no. 4: Substitute the value of n in the formula.
Position of Q2 =
1
2
(9+1)

23. Step no. 5: Simplify.
Position of Q2 =
1
2
(10)
Position of Q2 =
10
2
Position of Q2 = 5
Step no. 6: Locate the position of Q2 in the set of data.
1, 2, 4, 4, 5, 5, 6, 7, 8
The 5th value is 5 so Q2 = 5

24. Q1 Q2 Q3
1, 2, 4, 4, 5, 5, 6, 7, 8
Therefore:
• 25% of the students got the score ≤ 4.
• 50% of the students got the score ≤ 5.
• 75% of the students got the score ≤ 6.

25. ACTIVITY:
Answer the following. (5 points each)
1. Find the first, second and third quartile, given the scores of 10 students in their
Mathematics activity.
4, 9, 7, 14, 10, 8, 12, 15, 6, 11
2. Find the first, second and third quartile of the following numbers.
12, 5, 22, 30, 7, 36, 14, 42, 15, 53, 25

26. GROUP ACTIVITY:
Albert has an assignment to ask at random 10
students in their school about their ages. The data
are given in the table below.
a. What is Q1, Q2 and Q3 of their ages.

27. QUIZ:
A. Find the first quartile (Q1), second quartile (Q2) and third quartile (Q3) of the following. Show your
solutions completely. (5 pts.)
1. The owner of a coffee shop recorded the number of the customers who came into his café
each hour in a day. The results were
14, 10, 12, 9, 17, 5, 8, 9, 14, 10, and 11.
2. The score of 8 students in a mathematics seatwork are:
1, 11, 4 ,5, 6 ,7 ,2 ,8

28. ASSIGNMENT:
A. Find the first quartile (Q1), second quartile (Q2) and third quartile (Q3) of the following.
Show your solutions completely.
1. A group of students obtained the following scores in their math quiz:
4, 5, 5, 6, 2, 1, 4, 2, 9, 6, 7, 8, 3, 6, 3, 5, 8, 1, 1, 2, 5, 6, 7, 3, 5
B. What is Linear Interpolation and how is it useful in finding the measures of position of
quartiles? You may search in the internet and write your answer in your notebook.

29. Thank you!