Measures of central tendency ict integration

MEASURES OF CENTRAL
TENDENCY
MATH GROUP

Measures of Central Tendency
OBJECTIVES:
In this section, we’ll study to:
a. find averages, or “measures of central tendency”of a data set.
b. define and compute the Mean, Median and Mode
c. identify the appropriate use of mean, median, mode
MEAN MEDIAN

Central tendency
 A statistical measure
 A single score to define the center of a
set of scores/data

There are a variety of ways to measure
the central tendency of a data set.
The most popular is the mean, or arithmetic
average, which is found by adding all of the
data values and dividing by the total number
of values.
This is the most commonly
encountered type of central tendency
measure. The mean of a data set is
unique, and it is used in computing
other important statistics, such as the
variance. Here is the formula for
finding the sample mean:

For a population the Greek letter mu
For a sample mean
The ∑ (sigma) symbol (summation notation) indicates that
all the xi scores are added together and n the number of
scores.

The median is another measure of central
tendency, representing the halfway point in a
data set. Before you can find this point you must
first arrange the data set in
ascending/descending order and find the middle
point of the array (arranged data set).
The median is used when you need to find the
center or middle value of the data set.
Or when you need to find whether the data
values lie in the upper half or lower half of the
distribution. It is also used to find the average
of an open-ended distribution.

A third common measure of central tendency
is called the mode. This is the value that
most often occurs in the data set , sometimes
called the “ most typical” case.
A data set can have one mode (uni modal),
two mode (bi modal), or no mode at all.The mode is the easiest measure of
central tendency to compute.
However, a mode is not always unique
for a data set, and indeed may not even
exist.
The mode is used when the most
typical case is desired
and it can be used when the data
consist of word such as gender,
political party or religious
preference. It is not affected by
extreme data.

INTERACTIVE EXAMPLE
Tilapia in INRSF
Tilapia
Number
Length
(inches)
1 4.1
2 6.5
3 5.3
4 5.9
5 3.6
6 6.6
7 4.7
8 3.8
9 3.4
10 5.2
Press each button to calculate
mean, median and mode for the data set
MEAN
MEDIAN
Practice Test

4.1 + 6.5 + 5.3 + 5.9 + 3.6 + 6.6 + 4.7 + 3.8 + 3.4 + 5.2
10
49.1
10
4.91 Mean
MEAN
Click to go back
Tilapia
Number
Length
(inches)
1 4.1
2 6.5
3 5.3
4 5.9
5 3.6
6 6.6
7 4.7
8 3.8
9 3.4
10 5.2

MEDIAN
Click to go back
Tilapia
Number
Length
(inches)
1 4.1
2 6.5
3 5.3
4 5.9
5 3.6
6 6.6
7 4.7
8 3.8
9 3.4
10 5.2
Tilapia
Number
Length
(inches)
1 3.4
2 3.6
3 3.8
4 4.1
5 4.7
6 5.2
7 5.3
8 5.9
9 6.5
10 6.6
Arrange the data set in ascending order.
The median is located
between 4.7 and 5.2, hence
median is

Click to go back
The mode is the most
frequently occurring value
in the data set. In this data
set, no value occurs more
than once, so there is no
mode. Not every data has a
mode.
Salmon
Number
Length
(inches)
1 4.1
2 6.5
3 5.3
4 5.9
5 3.6
6 6.6
7 4.7
8 3.8
9 3.4
10 5.2

Practice 1 of 3
Find the mean of this data set of test scores;
2, 3, 6, 9, 10, 7, 7, 8, 9,9
6.3
7.0
7.7
None of the above

Find the mean of this data set of test scores;
5, 7, 9, 8, 2, 3, 4, 6
7.1
8
5.5
None of the above
Practice 2 of 3

Practice 3 of 3
What is are the proper measure(s) of central tendency, if
any to use in determining how high to make a bridge?
The distribution of the heights of the boats passing
under is known.
Mean
Median
Mode
none are proper

5 + 7 + 9 + 8 + 2 + 3 + 4 + 6
8
= 44
8
5.5

BACK
Hint: Find the mean using the formula;

2 + 3 + 6 + 9 + 10 + 7 + 7 + 8 + 9 + 9
10
70
10
7.0

Hint: Find the mean using the formula;

SORRY! Try again!

Excellent !

Solution: (D) none are proper
This problem requires some careful
thought; in building a bridge like this. No
average height is proper to use, because
average do not describe a population
fully.

Hint: The height of every boat that needs
to pass under must be considered.

Summary:
• The mean is the mathematical average
of a set of numbers.
• The mean is commonly referred to as
the “average.”
• The mean is quick and easy to calculate.
• The mean is easily influenced by
extreme values (very high or very low)
• The median is the middle
value of a set of data.
• Memorizing Tip: remember
that the median is in the
middle of the road.
The mode is the
most frequently
observed value
in a data set.

– The mean is appropriate for interval and ratio
variables.
– The mode is preferred for groups of data
which do not tend to group around a central
point.
– The median best measures the central
tendency of groups which contain extreme
values.
Choosing the Measure of Central
Tendency

1. Find the mean of the following test scores in
Math: 15, 21, 16, 17, 20, 21, 17 and 19.
2. The teacher gave five tests in Math. Bea got
the following scores in the 1st four tests: 82, 76,
79, and 81. What must be her score in the 5th
test so that her average is 80?
Solve the following problems.

1. Find the median of the set: 25, 28, 22, 20, 18, 23, 30, 24
2. Find the median score of 11 students in English test
6, 4, 9, 7, 3, 11, 12, 5, 10, 6, 8
3. Find the median of 8, 12, 5, 6, 13, and 15

1. Find the mode of the following set of data:
6, 4, 9, 7, 3, 11, 12, 5, 10, 6, 8
2. Find the mode of the test scores of 15
students
15 15 15 14 15 14 19 19 17 16 14 18 20 20
19

Measures of central tendency ict integration

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