Download Mean, Median, Mode and Range

Mean, Median and
Mode, and Range
Module 1, Lesson 4
Online Algebra 1
VHS@pwcs
Cami Craig
Numbers Everywhere
Numbers are a great way to
recognize trends and
interpret data. One way
to interpret is to use
measures of central
tendency. These are
mean, median, mode and
range.
Mean
The mean is one of the most common statistics that we
look at. You might know mean as the average.
To find the mean:
1. Add up all of the data
2. Divide by the number of items of data.
To find the mean of the numbers in the box above.
1. Add up all the data 0 + 1 + 2 + 3 + 5 + 7 = 18
2. Divide by the number of items of data: 18/6 = 3.
3. The mean or average is 3.
Median
The median is a number that is the middle when the numbers are in
order. How we find this is different if we have an even or odd
number of items in are data set.
For an odd number of items.
For an even number of items:
1.
Put the numbers in numerical order.
1.
Put the numbers in numerical order.
2.
Find the number in the middle, there will be
exactly one.
2.
There will be 2 numbers in the middle. Find
the sum of the 2 middle numbers and divide
by 2.
In the set of numbers:
In the set of numbers:
2, 3, 5, 5, 6, 8, 9, 9 12, 13, 14
There are 11 numbers, so our 6th number will
be the median. Notice that there are exactly 5
numbers on either side of 8, or 6th number.
1, 1, 2, 2, 4, 5, 8, 11
2 and 4 are in the middle. Notice that there are 3
numbers on each side of the 2 and 4.
The 2 + 4 = 6, and 6/2 = 3, so 3 is the median.
Mode
The mode is the number that occurs the
most.
In the set of numbers.
In the set of numbers:
8, 9, 2, 5, 6, 6, 2, 9, 9,6, 6
0, 1, 2, 4, 5, 7, 9, 3, 12
There are four 6’s therefore 6
is the mode.
There are no numbers that repeat.
Therefore there is no mode.
In the set of numbers:
2, 2, 3, 3, 4, 5, 6
There are two 2’s and two 3’s. In this case we have more than 1 mode.
The mode is both 2 and 3. (a double mode)
Range
 The range is the difference between the
greatest and the least values of a set of
data.
 Example: {6,3,10,14,2, 22,11}. The
greatest value is 22 and the least is 2.
The range is 22 – 2 which is 20.
 Example: {-10, 15, -32, 45, 23,20}. The
greatest value is 45 and the least is -32.
The range is 77. (45 - -32)
Try it!
Find the mean, median, mode, and range of each set of
numbers.
{23, 15, 17, 19, 23, 16, 34}
Mean: 21
{0, 20, 25, 42, 12, 25, 18,
22, 16, 32}
Mean: 21.2
Median: 19
Median: 21
Mode: 23
Mode: 25
Range: 19
Range: 42
Mean, Median, Mode & Range
Remember:
 The mean is the average of a set of numbers. To find it
add up the numbers and divide by the number of items
in the data set.
 The median is the number in the middle when the
numbers are in numerical order. If there is an even
number, you need to find the sum of the 2 middle
numbers and divide by 2.
 The mode is the number that occurs the most. There
can be one mode, no mode or more than one mode.
 The range is the difference between the greatest and
the least values in a set of data.
On your own
Homework is
Worksheet 1.4