This document defines and provides examples for measures of central tendency including mean, median, and mode. It explains that the mean is the average value found by summing all data points and dividing by the total number of data points. The median is the middle value when data points are arranged in order. The mode is the data point that occurs most frequently. It also discusses how to find the mean, median, and mode for grouped data using formulas and calculations involving class marks, frequencies, and cumulative frequencies.

1. MEASURES OF
CENTRAL
TENDENCIES

2. Ungrouped
data

4. Do you have an
idea what
MEAN(Statistics) is?


5. Mean
Is the average
value of a data.


6. Population Mean
Is the mean of the whole
population


7. Sample Mean
Is the mean of the part
of the population


8. Example Problems
1) The number of faculty
members in 10 different
colleges are 16, 25, 40, 24,
15, 20, 50, 15, 35 and 20.
Treating the data as a
population, find the population
mean of faculty members for

9. 2) The following are the ages of
the 9 children in a squatters
area. Find the mean.
Ages: 9, 8, 1, 3, 4, 5, 6, 7, 2

11. So,
what
is
median? Can you
give some ideas
about it?


12. Median
Is the value found at the
middle when the data are
arranged in an array form
from the highest to the
lowest or from the lowest to
the highest.


13. Example
1)
The
MEDIAN
x
9
8
7
6
5
4
3
2
1

14. 2)
x
9
8
7
6
5
4
3
2
1
1
The
MEDIAN

16. Mode
Is the value which
occurs most often or with
greatest frequency.


17. Example
1) The
MODE
x
10
9
9
7
6
5
3
2
1

18. 2)
x
18
18
17
17
17
17
16
16
16
15
15
17 and 16
The

19. grouped
data

20. What is a grouped
data?


22. In finding the mean in a
grouped data, we use
this formula:


23. Example
A
frequency
distribution of the
scores in English of
34
Education
students.


24. x
f
35 – 39
30 – 34
25 – 29
20 – 24
15 – 19
10 – 14
5-9
3
5
8
10
4
2
2
m
fm

25. x
f
m
fm
35 – 39
30 – 34
25 – 29
20 – 24
15 – 19
10 – 14
5-9
3
5
8
10
4
2
2
37
32
27
22
17
12
7
111
160
216
220
68
24
14

27. Where:
__– median
___– half sum
F – cumulative
frequency
f – frequency
i – interval

28. x
f
35 – 39
30 – 34
25 – 29
20 – 24
15 – 19
10 – 14
5-9
3
5
8
10
4
2
2
F

29. x
f
F
35 – 39
30 – 34
25 – 29
20 – 24
15 – 19
10 – 14
5-9
3
5
8
10
4
2
2
34
31
26
18
8
4
2

31. Where:
___ - mode
__ - median
__ - mean

32. Mean = 23.91
Median = 24
Find the mode using the
formula given.
