The document provides instructions for learning about measures of central tendency. It discusses finding the mean, median, and mode of ungrouped data. The mean is calculated by adding all values and dividing by the number of values. The median is the middle value when data is arranged in order. The mode is the most frequent value. Examples are provided to demonstrate calculating the mean, median, and mode of various data sets.

2. S
M
T
R
A
Stay focused.
Maintain a positive attitude.
Always come to school ready to learn
Respect one another
Try your best!
House Rules

3. Find Me
Direction:
Read each item and follow the given direction. Then, write
the letter of the correct answer in your paper.

4. 01
Find Allan’s average
grades in Mathematics by
adding all grades and
divide it by 4.
90 92 93 95
92
91
92.5
90
A
B
C
D

5. 02
Determine the number
that is located in the
middle of the given set of
data.
2 3 5 5 11
5
3
2
11
A
B
C
D

6. 03 A
B
C
D
Name the most numbered
fruit in the set
Apple
Orange
Strawberry
All are equal in number

8. Measures of Central
Tendency of Ungrouped
Data

9. At the end of the lesson, the learners should be able to do the following:
Learning Competencies
● Illustrate the measures of central tendency (mean, median, and
mode) of statistical data (M7SP-IVf-1).
● Calculate the measures of the central tendency of ungrouped and
grouped data (M7SP-IVf-g-1).

10. At the end of the lesson, the learners should be able to do the following:
Objectives
a. determine the mean, median and mode of ungrouped data;
b. appreciate the importance of central tendency of ungroup data by
participating in the class discussion; and
c. solve the mean, median and mode of ungrouped data in a considerable
speed and accuracy.

11. Let us say that your class took an exam in your math
class. You want to summarize the scores that you and
your classmates had as a single score. What score
should represent everyone’s score?

12. Is it the middle score of the entire class? Is it the most
common score in the class? How about if you add
everyone’s score and divide the score based on your
number?

13.  There are various ways on how to summarize the scores
of a ungroup data.
 These measures are called the measures of central
tendency.
 In this lesson, you will learn about the three measures of
central tendency—mean, median, and mode.

14. Essential Questions
● What is the difference between mean, median, and mode?
● What are some real-life scenarios where mean, median, or mode
are used?
● How do we choose which measure of central tendency should we
use when it is not explicitly stated in a word problem?

16. 01
Find Allan’s average
grades in Mathematics by
adding all grades and
divide it by 4.
90 92 93 95
92
91
92.5
90
A
B
C
D

17. Is the sum of all measurements divided by the number of
observations in the data set. This is also known as the “arithmetic
average”. So, to solve the mean. We have the given formula;
Mean
𝑥 =
Σ𝑥
𝑛
=
𝑥1 + 𝑥2 + 𝑥3 + ⋯ + 𝑥𝑛
𝑛
𝑥1 + 𝑥2 + 𝑥3 + ⋯ + 𝑥𝑛
𝑛
Data given
Total number of data
Note:

18. Example 1.
Find Anthony’s average grades in
Mathematics 7
1st grading period 92
2nd grading period 93
3rd grading period 95
4th grading period 95
𝑥 =
Σ𝑥
𝑛
=
𝑥1 + 𝑥2 + 𝑥3 + ⋯ + 𝑥𝑛
𝑛
𝑥 =
92 + 93 + 95 + 95
4
𝑥 =
375
4
𝑥 = 93.75
Solution:
∴ the mean of the ungrouped data is 93.75.

19. Example 2.
Find the mean of the ungrouped data: 1, 3, 10, 5, 2, 9.
𝑥 =
Σ𝑥
𝑛
=
𝑥1 + 𝑥2 + 𝑥3 + ⋯ + 𝑥𝑛
𝑛
𝑥 =
1 + 3 + 10 + 5 + 2 + 9
6
𝑥 =
30
6
𝑥 = 5
Solution:
∴ the mean of the ungrouped data is 5.

20. 02
Determine the number
that is located in the
middle of the given set of
data.
2 3 5 5 11
5
3
2
11
A
B
C
D

21. refers to the middle value in a set of quantities when arranged in
order
Median
To find the median of an ungroup data, there are some steps to
be followed;
1. Arrange the quantities either ascending or descending.
2. Number the quantities consecutively from 1 to n.
3. If n is odd, the median is the
n+1
2
th quantity
If n is even, the median is
𝑛
2
𝑡ℎ +
𝑛
2
+1 𝑡ℎ
2
quantities.

22. Example 1.
Find the median of the ungrouped data: 1, 3, 10, 5, 2, 9.
Solution:
1. Arrange the quantities either ascending or descending.
1, 2, 3, 5, 9, 10

23. Example 1.
Find the median of the ungrouped data: 1, 3, 10, 5, 2, 9.
Solution:
2. Number the quantities consecutively from 1 to n.
1, 2, 3, 5, 9, 10
=6 data

24. Example 1.
Find the median of the ungrouped data: 1, 2, 3, 5, 9, 10.
Solution:
3. If n is odd, the median is the
n+1
2
th quantity
If n is even, the median is
𝑛
2
𝑡ℎ+
𝑛
2
+1 𝑡ℎ
2
quantities.

25. Example 1.
Find the median of the ungrouped data: 1, 2, 3, 5, 9, 10.
Solution:
∴ the median of the ungrouped data is 4.
3. If n is even, the median is
𝑛
2
𝑡ℎ+
𝑛
2
+1 𝑡ℎ
2
quantities.
𝑀𝑑 =
𝑛
2
𝑡ℎ+
𝑛
2
+1 𝑡ℎ
2
𝑀𝑑 =
6
2
𝑡ℎ +
6
2
+ 1 𝑡ℎ
2
𝑀𝑑 =
3𝑟𝑑 + 4𝑡ℎ
2
𝑀𝑑 =
3 + 5
2
𝑀𝑑 =
8
2
𝑀𝑑 = 4

26. Example 2.
Find the median score of 9 students in English class.
30 19 17 16 15 10 5 2 32
Solution:
1. Arrange the quantities either ascending or descending.
2 5 10 15 16 17 19 30 32

27. Example 2.
Find the median score of 9 students in English class.
30 19 17 16 15 10 5 2 32
Solution:
2. Number the quantities consecutively from 1 to n.
2 5 10 15 16 17 19 30 32
=9 data

28. Example 2.
Find the median score of 9 students in English class.
2 5 10 15 16 17 19 30 32
Solution:
3. If n is odd, the median is the
n+1
2
th quantity
If n is even, the median is
𝑛
2
𝑡ℎ+
𝑛
2
+1 𝑡ℎ
2
quantities.

29. Example 2.
Solution:
∴ the median of the ungrouped data is 16.
3. If n is odd, the median is the
n+1
2
th quantity.
𝑀𝑑 =
𝑛 + 1
2
𝑡ℎ
𝑀𝑑 =
9 + 1
2
𝑡ℎ
𝑀𝑑 =
10
2
𝑡ℎ
𝑀𝑑 = 5𝑡ℎ
𝑀𝑑 = 16
Find the median score of 9 students in English class.
2 5 10 15 16 17 19 30 32

30. 03 A
B
C
D
Name the most numbered
fruit in the set
Apple
Orange
Strawberry
All are equal in number

31.  is the quantity with the most number of frequency or it refers to
the most frequent data in the set.
Common value in a set of data.
Mode
There are types of Mode;
1. Unimodal
2. Bimodal
3. Trimodal
4. Multimodal
5. No Mode

32. Mode
1. Unimodal
 A set data is unimodal distribution if it contains only one mode.
2. Bimodal
 A set of data is bimodal distribution if it contains two mode.
3. Trimodal
 a set of data is a trimodal distribution if it contains three mode
4. Multimodal
 a set of data is a multimodal distribution if it contains more than
three mode
5. No Mode

33. Example 1.
What is the mode of the ungrouped data given by 1, 3, 10, 5, 2, 9, 5 ?
Solution:
𝑀𝑜 = 5
∴ Unimodal

34. Example 2.
What is the mode of the ungrouped data given by 21, 18, 16, 21, 18, 20?
Solution:
𝑀𝑜 = 18 𝑎𝑛𝑑 21
∴ Bimodal

35. Example 3.
1, 2, 3, 2, 4, 5, 3, 2, 3, 6, 7, 8, 5, 5
Solution:
𝑀𝑜 = 2, 3 𝑎𝑛𝑑 5
∴ Trimodal

36. Example 4.
1, 1, 2, 2, 3, 3, 4, 4, 7, 7
Solution:
∴ No Mode

37. What is the mean of the set of values below?
11 19 27 25 2 12 29
Given the following data, find the median.
36 1 16 4 45 35 13
What is the mode of the set of values below?
59 57 74 61 61 57 64 61

39.  How to find the mean, media and mode of ungroup data?
 What are the steps in identifying the median of the given set of data?
 Why do we need to study the measures of central tendency?
 What are the importance of Measures of Central Tendency in our daily
life?

40. ● Ungrouped data is a set of data given as individual
values.
● The mean is the average value of a set of data. This is
the sum of all the values in the set of data divided by
the number of values.
o The mean of a sample (or the sample mean) is
and the mean of a population (or the population
𝜇 (mu).

41. o The formula for the sample mean is:
𝑥 =
Σ𝑥
𝑛
=
𝑥1 + 𝑥2 + 𝑥3 + ⋯ + 𝑥𝑛
𝑛
● The median is the middle value of a set of data when arranged in order.
o To find the median of even number of values, get the mean or
average of the two middle values.

42. ● The mode is the most frequent or common value in a set of data.
o To get the mode of the data set, we simply find the value that
appears most often. There could be more than one mode or no
mode at all in a given set of data.

43. Guess My Birthday
General Instructions
1. Create a four (4) groups from the population.
2. Next, Ask the group members to list down the birth date of each
member. (Ex: November 15 – the data needed is 15.)
3. Using the data gathered, find the mean, median and mode.
4. Write your answers on the given Cartolina.
5. Then, Present your output in front of the class.

44.  Solve the problems below.
1. Thalia is a doctor. She lists down the number of days 30 patients
are confined in a hospital. The number of days is shown below.
a. Find the average number of days that the patients are confined.
b. What is the median?
c. What is the mode?

45.  Agreement
a. Study in advance about the Measures of Central Tendency of
Grouped Data.

46. For Your Attention
THANK YOU
Hopefully, what we say can be useful
for all of you.