final demonstration

2. GRADE-7 AMETHYST~
FINAL
DEMONSTRATION
TEACHING
CATANDUANES STATE UNNIVERSITY
COLLEGE OF EDUCATION
Virac, Catanduanes
Pre-Service Teacher:
Maria Daniela Pereyra

3. Differentiate the
measures of central
tendency (mean,
median, and mode)
of a statistical data
Calculates the
measures of central
tendency of ungrouped
data.

5. Find some quiet
places.
Listen!
Look at the
screen
Answer when
teacher calls
your name
Enjoy the
discussion

9. S L T O

10. S O L U T I O N

11. P O L M

12. P R O B L E M

13. C O P T I N

14. C O M P U T A T I O N

15. I D L

16. M I D D L E

17. U

18. S U M

20. GRADE-7 AMETHYST~
Measures of Central
Tendency
of
Ungrouped Data
Teacher:
Maria Daniela Pereyra

21. Measures Central Tendency
-measure of central location
-it is a summary of measure that attempts
to describe a whole set of data with a
single value that represents the middle or
center of its distribution.

22. 3 MEASURES OF CENTRAL
TENDENCY
MODE
MEDIAN
MEAN

23. UNGROUPED DATA
Ungrouped Data is data given
as individual data points.
Example for this is a score of
15 students in exam.

24. UNGROUPED
DATA

25. CALCULATOR
PEN
PAPER

26. Player Age
Joebert 19
Zachari 20
Shara 20
Sarifa 21
Andrian 22
Joevin 22
Danilo 23
Daniela 23
Puriza 23
Presented on the table are
the ages of the Players.

27. M EA N ( 𝑥 )
The mean represents the average value
of the dataset. It can be calculated as
the sum of all numbers divided by the
total number of observations. In
general, it is considered as the
arithmetic mean.
Player Age
Joebert 19
Zachari 20
Shara 20
Sarifa 21
Andrian 22
Joevin 22
Danilo 23
Daniela 23
Puriza 23
193
1
2
3
4
5
6
7
8
9
21.4= ÷ 𝟗

28. Example for Mean:
Find the mean of the score of 8 students in a test.
23 25 30 19 21 23 28 25
𝑥 =
𝑥
𝑛
𝑜𝑟
𝑥= mean
𝑥= sum of all observations, read as the summation of X
n= total number of observations in the data
𝑥 =
𝑥
𝑛
=
23 + 25 + 30 + 19 + 21 + 23 + 28 + 25
8
= 24.25
mean=
𝑆𝑢𝑚 𝑜𝑓 𝑂𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑂𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠
FORMULA:

29. M EDIA N ( 𝑥)
We determine the median, denoted
as 𝑥 ,usually referred to midpoint,
of a given data by following these
steps:
Step 1:
The data should be
arranged from least to
greatest.
Player Age
Joebert 21
Zachari 20
Shara 20
Sarifa 23
Andrian 21
Joevin 20
Danilo 23
Daniela 23
Puriza 21

30. M EDIA N ( 𝑥)
Step 2:
If there is an "odd number" of
observation, the
median is the middle
data point.
Player Age
Joebert 19
Zachari 20
Shara 20
Sarifa 21
Andrian 22
Joevin 22
Joevin 23
Daniela 23
Myla 23

31. Step 3:
If there is an “even number” of
observations, the median is
the average of the two
middle data points.
M EDIA N ( 𝑥)
Player Age
Joebert 19
Zachari 20
Shara 20
Sarifa 21
Andrian 22
Joevin 22
Danilo 23
Daniela 23
Puriza 23
John Paul 25
(22+22)÷ 2= 22

32. Example for Median:
Find the median of the given scores.
19 21 23 23 25 25 28 30
23 25 30 19 21 23 28 25
And get the average of the two middle numbers.
𝑥 = 23 + 25 ÷ 2
Arrange the scores from least to greatest.
= 24

33. M ODE (𝑥)
The mode of a data is the
data that occurs most
often. the mode is the
given data in the table is
23. it occurs 3 times.
Player Age
Joebert 19
Zachari 20
Shara 20
Sarifa 21
Andrian 22
Joevin 22
Danilo 23
Daniela 23
Puriza 23
If no number is repeated then
the data has no mode.

34. 1. Unimodal
4 types of mode
2. Bimodal
3. Trimodal
a collection of data/number s with one mode
a set of data including two modes is identified
as a bimodal model.
4. Multimodal
a collection of data including three modes
a set of data including four or more than four
modes.

35. Example no.1:
1, 2, 3, 4, 5, 5, 5, 6, 6, 6, 7, 7, 9
Example no.2:
1, 2, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7
Mode: 5 and 6
Mode:
Type of mode: Bimodal
Type of mode: Trimodal
4, 5, and 6

36. Example no.3:
19, 20, 20, 21, 21, 22, 22, 22, 23, 24, 25
Mode: 22
Type of mode: Unimodal

37. Example no.4:
19, 20, 20, 21, 21, 22, 22, 23, 24, 24, 25,25
Mode: 20, 21 22, 24, and 25
Type of mode: Multimodal

38. 𝑥
Example for Mode:
Find the mode of the given scores in Example 2. The
mode is usually denoted as 𝑥
𝑥= 23 and 25
19 21 23 23 25 25 28 30
BIMODAL

39. The Mode
shows upthe
most.
The Median
is the middle.
Here's an easy way to remember--
The Mean is
the average.

40. 𝑥
The mean, median, and mode computed from the
raw or ungrouped data, also called primary data, are
exact values. When the set of primary data is not
available, we just estimate the values of the
measures of central tendency using available data,
like the grouped data. Grouped data are considered
secondary data.

41. Activity: Find me!
Find the mode of the
following set of data.
mean
,
median and

42. Find the mean, media, and mode
Scores of joey in his mathematics test.
75 78 82 82 92 96
MEAN :________________________
MEDIAN:______________________
MODE:________________________
84.16
82
82
82 75 92 96 78 82

43. Find the mean, media, and mode
The cost of a can of milk from different stores
₱18.50 ₱17.50 ₱18.00 ₱19.00 ₱20.25
MEAN:________________________
MEDIAN:______________________
MODE:________________________
₱ 18.65
₱18.50
₱17.50 ₱18.00 ₱18.50 ₱19.00 ₱20.25
If no number is repeated then the
data has no mode.

44. Find the mean, media, and mode
Number of students in each class in a small school
20 15 20 22 18 17 19 19 20 21 20 20
MEAN:________________________
MEDIAN:______________________
MODE:________________________
19.25
20
15 17 18 19 19 20 20 20 20 20 21 22
20

46. Evaluation:
Identify the following.
1.It is the middle value.
2.It is commonly called the average.
3.Sometimes called the midpoint value.
4.Most repeating value in the set.
Find the mean, median, and mode for each
set of data.
6. 88, 78, 90, 94 90, 84, 90
7. 100, 200, 100, 300, 300, 200 150, 100.
8. 1.52, 1.36, 1.34, 1.56, 1.76, 1.52, 1.52

47. Assignment:
Find the mean, median, and mode for each set of data.
1.88, 78, 90, 94, 90, 84, 90, 98,
2.100, 200, 100, 300, 300, 200, 200, 150, 100
3.1.52, 1.36, 1.34, 1.56, 1.76, 1.52, 1.52

48. THANK YOU FOR
LISTENING!
Don't hesitate to ask any questions!