This document defines and provides examples of three common measures of central tendency: the mean, median, and mode. The mean is the average found by adding all data points and dividing by the total number. The median is the middle number when data points are ordered from lowest to highest. The mode is the most frequently occurring data point in a dataset. Examples are provided to demonstrate how to calculate each measure using sample data sets.

1. MEASURES OF
LOCATION
By Aqsa Memon

2. Definition
◦Summarizing data can help us understand them,
especially when the number of data is large. Measure
Of Location presents several ways to summarize
quantitative data by a typical value.

3. ◦We will study three common measures of location:
◦the MEAN,
◦THE MEDIAN,
◦AND THE MODE.
◦THE MEAN, MEDIAN AND MODE ARE ALL "MOST
REPRESENTATIVE

4. The Mean
◦The mean (more precisely, the arithmetic mean) is
commonly called the average. It is the sum of the data,
divided by the number of data:
◦ Mean: The "average" number; found by adding all data points and dividing by
the number of data points.
Mean= sum of data
-------------------------- = Total Number of data
Number Of data

5. Example of Mean
Example: The mean of 4, 1, and 7 is (4+1+7)/3=12
Calculating the mean
There are many different types of mean, but usually when people
say mean, they are talking about the arithmetic mean.
Here's the same formula written more formally:
Mean= ∑xi
____
n

6. The Median
◦ Median: The middle number; found by ordering all data
points and picking out the one in the middle (or if there are
two middle numbers, taking the mean of those two
numbers).
◦ Example: The median of 444, 111, and 777 is 444 because
when the numbers are put in order (1(1(1, 444, 7)7)7), the
number 444 is in the middle.

7. Finding the Median
◦ The median is the middle point in a dataset—half of the data points
are smaller than the median and half of the data points are larger.
◦ To find the median:
◦ Arrange the data points from smallest to largest.
◦ If the number of data points is odd, the median is the middle data
point in the list.
◦ If the number of data points is even, the median is the average of the
two middle data points in the list.

8. Example 1
◦ Find the median of this data:
1, 4, 2, 5, 0
◦ Put the data in order first:
0, 1, 2, 4, 5
◦ There is an odd number of data points, so the median is the
middle data point.
◦ 0, 1,2 , 4, 5
◦ The median is 2.

9. The Mode
◦ Mode: The most frequent number—that is, the number that
occurs the highest number of times.
◦ The mode is the most commonly occurring data point in a
dataset. The mode is useful when there are a lot of repeated
values in a dataset. There can be no mode, one mode, or
multiple modes in a dataset.

10. Example Of Mode
Ms. Norris asked students in her class how many siblings they
each had.
Find the mode of the data:
0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 5
Look for the value that occurs the most:
0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2 ,3, 5
The mode is 1 sibling.