1.
Measures Of Central Tendency
(Grouped Data)
• Measure of central tendency are defined for a population (large set of
objects of a similar nature) and for a sample (portion of the elements of
a population).
• A measure of central tendency is a value that describes a data set. It is a
measure that tells us where the data tends to be clustered. It allows us to
locate the "center of gravity" of a distribution.
• In statistics, a central tendency is a central value or a typical value for
a probability distribution. It is occasionally called an average or just
the center of the distribution. The most common measures of central
tendency are the arithmetic mean, the median and the mode.
 Introductio
n

2.
• Define measure of central tendency (mean, median
and mode).
• Find the measures of central tendency using grouped
data.
a. Find the mean, median and mode of grouped data.

3.
 A measure of central tendency is a typical value
around which other figures gather.(Simpson and
Kafka)
• An average stands for the whole group of which it forms a
part yet represents the whole. (Waugh)
• It is an average. It is a single number of value which
can be considered typical in a set of data as a whole.
(layman’s term)

4.
 To find representative value
 To make more concise data
 To make comparisons
 Helpful in further statistical analysis

5.
• The mean of a set of values or measurements is the sum of the
measurements divided by the number of measurements in the set. It is
the most popular and widely used. It is sometimes called the arithmetic
mean.
X

6.
Compute the mean of the scores of the students in a Mathematics IV test.
Class Frequency X fX
46-50 1
41-45 5
36-40 11
31-35 12
26-30 11
21-25 5
16-20 2
11-15 1 13
48
18
23
28
33
38
43
48
215
418
396
308
115
36
13
Total 48 1,549

7.
• The median is the middle value in a set of quantities. It separates an
ordered set of data into two equal parts. Half of the quantities found
above the median and the other half is found below it.

8.
Compute the median of the scores of the students in a Mathematics IV test.
Class Frequency lb <cf
46-50 1
41-45 5
36-40 11
31-35 12
26-30 11
21-25 5
16-20 2
11-15 1 10.5
45.5
15.5
20.5
25.5
30.5
35.5
40.5
48
47
42
31
19
8
3
1
Total 48
48
2 = 24th

9.
Compute the median of the scores of the students in a Mathematics IV test.
Class Frequency lb <cf
46-50 1
41-45 5
36-40 11
31-35 12
26-30 11
21-25 5
16-20 2
11-15 1
35.5
47
8
45.5
15.5
20.5
25.5
30.5
40.5
48
42
31
19
1
10.5
3
Total 48

10.
• The mode of grouped data can be approximated using the following
formula:

11.
Compute the mode of the scores of the students in a Mathematics IV test.
Class Frequency lb
46-50 1
41-45 5
36-40 11
31-35 12
26-30 11
21-25 5
16-20 2
11-15 1
35.5
45.5
15.5
20.5
25.5
30.5
40.5
10.5

12.
 Mean can be calculated for any set of numerical data, so it always exists.
 A set of numerical data has one and only one mean.
 Mean is the most reliable measure of central tendency since it takes into
account every item in the set of data.
It is greatly affected by extreme or deviant values (outliers)
 It is used only if data are interval or ratio.

13.
 It is used when you want to find the value which occurs most often.
 It is a quick approximation of the average.
 It is inspection average.
 It is the most unreliable among the three measures of
central tendency because its value is undefined in some
observations.)

14.
 It is used when you want to find the value which occurs most often.
 It is a quick approximation of the average.
 It is inspection average.
 It is the most unreliable among the three measures of central
tendency because its value is undefined in some observations.)

15.
• Mode is readily comprehensible and easily calculated.
• It is the best representative of data.
• It is not at all affected by extreme value.
• The value of mode can also be determined graphically.
• It is usually an actual value of an important part of the series..

16.
• It is not based on all observations..
• It is not capable of further mathematical manipulation.
• Mode is affected to a great extent by sampling fluctuations.
• Choice of grouping has great influence on the value of mode.

17.
• Median can be calculated in all distributions.
• Median can be understood even by common people.
• It can be located graphically.
• It is most useful dealing with qualitative data.

18.
• It is not based in all the values.
• It is not capable of further mathematical treatment.
• It is affected fluctuation of sampling.
• In case of even number of values, it may not the value from the
data.

19.
A measure of central tendency is a measure that tells us where the
middle of a bunch of data lies.
Mean is the most common measure of central tendency. It is simply
the sum of the numbers divided by the number in a set of data. This
is also known as average.
Median is the number present in the middle when the numbers in a
set of data are arrange in ascending or descending order. If the
number of numbers in a data set is even, then the median is the
mean of the two middle numbers.
Mode is the value that occurs most frequently in a set of data.