Transcript Measures of Central Tendency

Measures of Central
Tendency
Mean, Median, Mode, and Range
Mean
Also called the average
 Times we use the mean in the real-world:

 Class averages on tests/quizzes
 Sports – baseball, basketball, football
 Groceries
How to calculate the mean
Add up all data
 Divide the sum by the number of data
items
 EXAMPLE:

 3, 4, 6, 7, 8, 2,
 SUM is 3+4+6+7+8+2 = 30
 30 divided by 6 (number of data items) = 5
 The mean (average) is 5

Solve examples on the board
Median
“Median” means middle
 When driving down the highway, stay
away from the median!

 That is the middle of the road!
How to find the median
Put all data in order from least to greatest.
 Then find the number that is in the
middle!
 EXAMPLE: 4, 3, 5, 7, 1, 2, 9

– IN ORDER: 1, 2, 3, 4, 5, 7, 9
– The middle number is 4!
– The median is 4!
But …

What if you have two medians?!
– EXAMPLE: 2, 1, 3, 4, 6, 3, 2, 1, 8, 5, 4, 9
– In order: 1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 8, 9
– The two medians are 3 and 4 BUT – you
cannot have 2 medians!
– To find the real median, you add the two
together (3+ 4 = 7), and divide by 2.
– SO… 7 ÷ 2 = 3.5. The median is 3.5!

EXAMPLES on the board!
Mode
The mode is the number (or numbers)
that occur(s) the most!
 HINT: Mode sounds like Most!
 It helps to put the numbers in order from
least to greatest, just like we do finding
the median!

Finding the mode

Example: 3, 2, 5, 6, 1, 2, 2, 3, 8
– In order: 1, 2, 2, 2, 3, 3, 5 ,6, 8
– The number that shows up the MOST is 2! So the
MODE is 2!

BUT… what about this: 2, 3, 4, 3, 2, 1, 6, 5, 4
– In order: 1, 2, 2, 3, 3, 4, 4, 5, 6
– 2, 3, and 4, all show up twice while the other
numbers show up only once each. SO… the modes
are 2, 3, and 4!
More on modes

What would I do in this situation?
– 1, 2, 3, 4, 5, 6, 7, 8
– NONE of the numbers show up more often
than any other.
– There is NO mode!

Examples on the board!
Range
The range is the spread of the data.
 To find the range, we take the largest
number and subtract the smallest number.
 EXAMPLE: 2, 4, 6, 3, 1, 9, 5, 2, 2, 3

 Largest: 9
 Smallest: 1
 Range = 9 - 1 = 8
 The range is 8!