Transcript 09 Analyzing the Data - Mean, median and mode

Analyzing the Data:
Calculating Mean, Median & Mode
After all of the research has been conducted,
the next step in the research process is that of
analyzing the data to see if any “correlations” or
relationships that exist between any 2 or more
elements
In order to make sense of the data, researchers use a variety
of mathematical tools to help summarize the information.
The three most common are:
Mean
Mode
Median
Let’s take a look at each……..
1. Mean
Formula:
Mean = sum of elements / number of elements
Example: To find the mean of 3,5,7.
Step 1: Find the sum of the numbers.
3+5+7 = 15
Step 2: Calculate the total number.
there are 3 numbers.
Step 3: Finding mean.
15/3 = 5
2. Median
•
Median is the middle value of the given numbers or
distribution
Example: To find the median of 4,5,7,2,1
Step 1: Count the total numbers given.
There are 5 elements or numbers in the distribution.
Step 2: Arrange the numbers in ascending order.
1,2,4,5,7
Step 3:
Choose the element in the middle
Example: For an odd number set (1,2,4,5,7) look for the middle element
4 is the median
Example: For an even number set (1,2,4,5,7,9), look for the two middle
elements and take their average
4+5=9/2 = 4.5
4.5 is the median
So….what’s the difference between median and mean?
Aren’t they the same thing, just looking for the middle
number?
Well, the answer is “no”, they’re different….let’s look at an
example:
Let’s look at a Grand River Transit bus. At a given time, five
people are riding it…..here is their income distribution:
$ 70,000
$ 60,000
$ 50,000
$ 40,000
$ 30,000
The “mean” income of those riders is $50,000 a year (add up the
salaries and divide by the number of salaries).
$70,000 + $60,000 + $50,000 + $40,000 + $30,000
= $250,000 / 5
= $50,000
If we calculate the median income of those riders, it is also
$50,000 a year.
= $70,000 / $60,000 / $50,000 / $40,000 / $30,000
• So, you get the same answer….why do both ??
•OK…let’s analyze a different scenario…..
•Joe Blow gets off the bus. Bill Gates gets on.
Here is the new income distribution:
$ 50,000,000
$ 60,000
$ 50,000
$ 40,000
$ 30,000
• The median income of those riders remains
$50,000 a year
$50,000,000 / $60,000 / $50,000 / $40,000 / $30,000
But the mean income is now somewhere in the neighborhood of
$10 million or so.
$50,000,000 + $60,000 + $50,000 + $40,000 + $30,000
= $50,180,000 / 5
= $10,036,000
•By using the “mean”, the “average” income of those bus
riders is just over 10 million dollars
• As a result, we need to calculate both the “mean” and
“median” and then use them in context to what we are
researching
• In this case, using the “median” rather than the “mean” would
provide a much more representative and accurate picture of
those bus riders' place in the Kitchener economy
3.
Mode
The mode is the most frequently occurring value in a frequency
distribution.
Example: To find the mode of 11,3,5,11,7,3,11
•Step 1:
Arrange the numbers in ascending order.
3,3,5,7,11,11,11
Step 2:
In the above distribution:
Number 11 occurs 3 times,
Number 3 occurs 2 times,
Number 5 occurs 1 times,
Number 7 occurs 1 times.
So the number with most occurrences is 11 and is the Mode
of this distribution.
Note: If all of the elements only occur once, there is no
mode.
•
As a result, a researcher will use the mean, median and
mode to help decipher and interpret the raw data they
have collected
•
The element(s) that is utilized to interpret the data
depends on the context of the research and what
interpretation “makes the most sense”
The End !!