1. Measures of central tendency
Dominique Warmsley
&
Bettina Bonsu
March 29, 2010
Math 300-003

2. When you hear someone use the wordaverage to describe a set of numbers, there are 3 ways you can describe data, allof which can bethought of as measures of central tendency
1. Mean
2. Median
3. Mode
3. Mean: A set of numbers is the sum of values dividedby the number of values. We can write this as a formula.
Example:
These are thevalues
5 + 10 + 7+ 12 + 8 + 6= 48
Add all the numbers
Then count all the values and then divide by number of
values.
48 divided by 6 = 8
So the mean for this set of values is 8
4. Work It out!
What is the Mean of this set 7,10, 8, 14, 6
Remember: follow all the steps!
5. Answer is:
7 + 10 + 8 + 14+ 6= 45
45 divided by 5 is 9
So your mean is 9
6. Median:a middle number of a set of numbers. You have to make sure your numbers are in order first.
Values need to be orderedleast to greatest.
If the number of datavalues in the list is odd, then
the median is the middle number in the list.
If the number of data value is even, there is no single middle
number . So the median is themeanofthe 2 middle numbers in the list.
7. Watch Me!!!
Example:
35, 74, 53, 98, 32,
Place in order least to greatest
32, 35, 53, 74, 98
The median is 53
There are 5 values (an odd #), so the median is the middle number.
8. Now Ill watch you!
4200, 3600, 4500, 3500, 3800
Now put them in order, and find your
median
9. See it wasnt that hard
The order least to greatest
3500, 3600, 3800, 4200, 4500
Becausethere are five data values
(an odd number) the middle number is
median. 3800 is the median. But you knew
thatright.
10. It can also look like this ..
2600, 3900, 9800, 2200, 4100, 1500
Next step is least to greatest
1500, 2200, 2600, 3900, 4100, 9800
The middle # are.. 2600, 3900
you add both numbers 2600 +3900 = 6500
Then6500 divided by 2 = 3250
Remember these steps.
11. Now you can try this..
Find the median of this value set:
26.08, 39.02, 98.07, 22.03, 41.04, 15.02
12. Solution..
Find the median of this value set:
26.08, 39.02, 98.07, 22.03, 41.04, 15.02
In order from smallest to largest:
15.02, 22.03,26.08, 39.02, 41.04 ,98.07
Taking the mean of the middle two values
26.08 + 39.02= 65.1
65.1 divided by 2= 32.55
13. Mode: set ofa valuethat occur most often.
If two values occur most often we say the data is a bimodal.
If more than two values occur most often, we say there is no mode.
14. Data Sets
Example1:
6.3, 12.5, 2.3, 6.3, 1.2, 3.3, 6.3,
The data value 6.3 appears more often
then any number . Therefore 6.3 is the
mode.
Example 2:
2, 12, 14, 67, 98, 6, 15, 13, 10
No data value occurs most often, There is
no mode for this set.
15. Now you can try this..
Find the mode of the value sets :
Pink, blue, silver, yellow, pink , blue , pink
6, 14, 13, 12, 14, 6, 5, 6, 10, 14, 2
2, 5, 10,3, 6, 19, 11, 20, 19
16. Solution
Find the mode of the value sets :
Pink, blue, silver, yellow, pink , blue , pink
Mode is: pink
6, 14, 13, 12, 14, 6, 5, 6, 10, 14, 2
Bimodal sets are: 6, 14
2, 5, 10, 3, 6,9, 11, 20, 19
Mode is: none
17. Food For Thought!
So, remember when you think average,
think a set a numbers .
And revisit your friends :
Mean
Median
Mode
Remember math is your friend !
Give him a hug