3. What is Central Tendency?
Measures of Central Tendency:
- one type of summary statistic
- are measures of location within a distribu-tion
- A measure that tells us the middle of a bunch of data
lies
- 3 most common measures of central tendency are
mean, median, mode

4. Importance of the Measures of Central
Tendency
•
•
•
•
To find representative value
To condense data
To make comparisons
Helpful in further statistical analysis

5. MEAN

6. Example:
The marks of seven students in a mathematics test with a
maximum possible mark of 20 are given below:
15 13 18 16 14 17 12
Find the mean of this set of data values.
Solution:
15

7. MEDIAN
• The median (mdn) of a set of data values is
the middle value of the data set when it has
been arranged in ascending order. That
is, from the smallest value to the highest
value.

8. Note:
• If the list has an odd number of entries, the
median is the middle entry in the list after sorting
the list into increasing order.
Example:
The marks of nine students in a geography test that
had a maximum possible mark of 50 are given
below:
47
35
37
32
38
39
36
34
Find the median (mdn) of this set of data values.
35

9. Solution:
Arrange the data values in order from the lowest
value to the highest value:
32 34 35 35 36 37 38 39 47
The fifth data value, 36, is the middle value in this
arrangement.
.: mdn = 36
Formula:

10. Note:
In
32
34
35
Mdn = 5th value
Mdn = 36
Mdn =
35
36
37
38
39
47

11. Note:
If the list has an even number of entries, the
median is equal to the sum of the two middle (after
sorting) numbers divided by two.
Example:
The marks of eight students in a math test that had a
maximum possible mark of 20 are given below:
12 18 16 21 10 13 17 19
Find the median of this set of data values.

12. Solution:
Arrange the data values in order from the
lowest value to the highest value:
10
12
13
16
17
18
19
21
The number of values in the data set is 8, which
is even. So, the median is the average of the
two middle values.

15. MODE
• For lists, the mode is the most common
(frequent) value.
• A data set has no mode when all the numbers
appear in the data with the same frequency.
• A data set has multiple modes when two or
more values appear with the same frequency.

16. Example:
Find the mode of the following data set:
48 44 48 45 42 49 48
The mode is 48 since it occurs most often.

17. Example:
The test scores of 9 seventh grade students are
listed below. Find the mode.
82, 92, 75 , 91, 92, 89, 95, 100, 86
The mode is 92 since it occurs most often.

18. Note:
• It is possible for a set of data values to have
more than one mode.
• If there are two data values that occur most
frequently, we say that the set of data values
is bimodal.
• If there is no data value or data values that
occur most frequently, we say that the set of
data values has no mode.