This document discusses calculating quartiles of a data set. It begins by defining key terms like quartiles, data, ungrouped data, and measures of position. It then explains how to find the quartiles using the Mendenhall and Sincich method, which involves arranging data in order and using a formula to determine quartile positions. The document provides examples of calculating the lower and upper quartile differences for different data sets. It concludes by generalizing the process and evaluating example problems of finding individual quartiles and their sum.

2. Activating Prior
Knowledge
1. What is statistics about?
2. What is Survey?
3. What are the different between
population, sample, and sample size?

3. Do you familiar with measure of central
tendency? Or Mean, Median, and Mode?
Measures of Central Tendency
Mean Median Mode

4. Activity

5. Measure

6. Position

7. Show

8. Reason

9. 1. What did you observed on the game?
2. What do you call a data that is not
grouped?
Questions:

11. Learning Objectives
•Illustrate the quartiles for ungrouped
data
•Calculate the first quartile, second
quartile and third quartile of a set of data.
•Appreciate the concept of this topic in
real-life situation.

12. Group Activity

13. Procedure
1. Arrange the data in INCREASING or DECREASING
order.
2. Identify the lowest score and highest score.
3. Find the middle score. Level it as Q2
4. Identify the value between the middle score and
the lowest score. Level it as Q1.
5. Identify the value between the middle score and
highest score. Level it as Q3.

14. Questions
•What is Q1, Q2, and Q3 of the data?
•How many data belong to Q1, Q2, and Q3
in terms of data?
•Have you realize of finding the position of
the data?

15. Group 1: The number of games won by famous
basketball team each year from the year 1991 to the year
2000 are 20, 25, 20, 45, 45, 30, and 35.
Group 2: The rate of an article changed in six consecutive
months. Its rate each month was 16, 13, 11, 8, 18, and 3.
Group 3: The owner of a supermarket recorded the
number of customers who came into his store each hour
in a day. The results were 11, 7, 9, 6, 14, 11, and 8.
Group 4: Find the average of the lower, middle, and the
upper quartile of the data. 15, 18, 23, 6, 7, 22, and 12.

17. What is measure
of position?
Tells where a
specific data value
falls within the
data set or its
relatives position
in comparison with
other data values.

18. What is data?
It is a factual
information (such as
measurements or
statistics) used as a
basis for reasoning ,
discussion, or
calculation.

19. What is Ungroup
data?
The data you first
gather from an
experiment or study
which not sorted
into categories,
classified, or
otherwise grouped.

20. What is quartile?
The quartiles are
the score points
which divide a
distribution into
four equal parts.

21. 25% 50% 75% 100%
Q1 Q2 Q3
Lower
Quartile
Middle
Quartile
Upper
Quartile

22. What is quartile?
If the number of the
scores is even, the
median is the
average of the two
middles score.

23. Finding the Quartiles
a. Arrange the data in ascending order
b. Using Mendenhall and Sincich Method
c. Locate the values of the specified
quartile using interpolation method.

24. Mendenhall and Sinchich Method
A method of finding the quartile value.
Where, Q is quartile, k is number of quartile, and n
is number of data.

25. Interpolation method
a. Find the difference between the two values
wherein, Q1 is situated.
b. get the decimal part result in quartile and
multiply it with the result in step a.
c. Add the result in the step b to the smallest
number wherein Q1 is situated to get the
position of Q1.

26. Example 1:
Calculate the position of the lower quartile in
the given data {2, 5, 7, 10, 9, 3, 2, 11, 4, 12}
Finding the quartiles
a. Arrange the data in ascending order
b. Using Mendenhall and Sincich Method
c. Locate the values of the specified quartile.

27. Interpolation method
a. Find the difference between the two values
wherein, Q1 is situated.
b. get the decimal part result in quartile and
multiply it with the result in step a.
c. Add the result in the step b to the smallest
number wherein Q1 is situated to get the
position of Q1.

28. Example 2:
The numbers of game won by famous basketball
team each year from the year 1991 to the year
2000 are 20, 25, 20, 45, 35, 50, 35, 45, 30, 60, and
35. Find the difference between of the lower
quartile and the upper quartile of the data set.
Finding the quartiles
a. Arrange the data in ascending order
b. Using Mendenhall and Sincich Method
c. Locate the values of the specified quartile.

29. Try this!
The rate of an article changed in six consecutive
months. Its rate each month was 16, 13, 11, 8, 18,
and 3. Find the difference between of the lower
quartile and the upper quartile of the data set.

30. Generalization
Students Name Grades
Villar 91
Calpaya 97
Bantilan 89
Haban 71
Magbanua 69
Apostol 50
Alelojo 100
How many students is in 75%?

31. Generalization
1. What is Quartile?
The quartiles are the score points which divide a
distribution into four equal parts. If the number of
the scores is even, the median is the average of the
two middles score.
2. How to calculate Quartile of a set of data?
Using the formula, Q=k/4(n+1). Where, Q is
quartile, k is number of quartile, and n is number of
data.

32. Evaluation
Evaluate the following problem.
1. Calculate Quartile-3 from the following data 3,
13, 11, 15, 5, 4, 2.
2. Annie conducted a math test for her students.
The scores they got in the test are 16, 19, 9, 14,
31, 9, 24, 16, 19, 14 and 31. Find the sum of
lower quartile, middle quartile, and upper
quartile.

33. Evaluation
Evaluate the following problem.
1. Calculate Quartile-3 from the following data 3,
13, 11, 15, 5, 4, 2.
Sol: {2, 3, 4, 5, 11, 13, 15}, n=7
Q3 = k/4(n+1) Q3 = ¾(7+1)
= 24/4
= 6  6th position Q3 = 13

34. 2. Sol: {9, 9, 14, 14, 16, 16, 19, 19, 24, 31, 31}, n=11
Q1= ¼(n+1) Q2 = 2/4(n+1)
= 12/4 = 24/4
= 3 3rd position = 6  6th position
Q1 = 14 Q2 = 16
Q3 = ¾(n+1) Q1 +Q2 +Q3 = 14 +16 +24
= 36/4 = 54
= 9  9th position
Q3 = 24

35. Thank
You!