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Measures of Central
Tendency
Measure of central tendency – A value that represents the
centre of a data set, can be the mean, median or mode.
Data Set – A collection of numbers
Ex: [9,13,12,8,8] is a data set
Mean
The “mean” is computed by adding all of the numbers in
the data together and dividing by the number of elements
contained in the data set.
Example:
Data Set = 2, 5, 9, 3, 5, 4, 7
Number of Elements in Data Set =
Mean =
Median
The “median” of the data set depends on whether the
number of elements in the data set is odd or even. Steps
to find the median:
1. Reorder the data set from smallest to largest.
2. If the number of elements is odd the median is the
middle number.
3. If the number of elements is even the median is the
average of the two middle numbers.
Median
Example #1: Example #2:
Find the median of the Find the median of the
data set: data set:
9,13,12,8,8 6,2,7,19,13, 9
Written in increasing Written in increasing
order = order =
8, 8, 9, 12, 13 2, 6, 7, 9, 13, 19
Median = 9 Median =
(7+9) ÷ 2 = 8
Mode
The mode for a data set is the element that occurs the most
often. It is not uncommon for a data set to have more than one
mode. Some sets have no mode.
Example #1:
[9,13,12,8,8]
Mode = 8
Example #2:
[6,2,7,19,13, 9]
Mode = no mode
Example #3:
[2,2,6,8,7,9,8]
Mode = 2 and 8
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