Mean, Median, Mode, 5 number Summary, and Center of Dispersion

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MEAN, MEDIAN, MODE, 5 NUMBER
SUMMARY, AND CENTER OF DISPERSION
WARM UP

Decide if it’s a permutation or a combination, then
find how many are possible:

Your class is having an election. There are 7
candidates, and they are each running for president,
vice president, secretary, and treasurer. How many
different executive boards are possible?

The 3 students who did not win office decided to run for
representative with 12 other students. If there are 10
representative positions available, how many different
student councils are possible?
MEAN
Another word for average
 Also called “x-bar” (especially when we talk
about statistics)


You find this by adding up all the numerical
data in a set and dividing it by the number of
data entries in the set
EXAMPLE
Find the Mean for the following set:
 48, 23, 97, 36, 27, 72, 48, 41, 58

 48+23+97+36+27+72+48+41+58=450
 450/9=50,
so 50 is the mean
Find x bar for the following set:
420, 360, 398, 196, 398, 400
A.) 300
B.) 312
C.) 362
D.) 398
E.) 400
Uploading Graph
MEDIAN
After numbers are written in numerical order,
the median is the middle number
 Does it matter if the numbers increase or
decrease?

 We
normally write them in increasing order, but it
doesn’t actually matter
EX

Find the median of this set:
 48,
23, 97, 36, 27, 72, 48, 41, 58
 Remember
the first step is to list in order:
 23, 27, 36, 41, 48, 48, 58, 72, 97
 There
are 9 numbers, so the 5th number is the middle:
48 is the median
00:00:28
Find the median of the set:
420, 360, 398, 196, 398, 400
A.) 360
B.) 362
C.) 196
D.) 400
E.) 398
Uploading Graph
MODE
The most frequent number or numbers
 There can be no mode
 There can be multiple modes

EX
Find the mode of this set of data
 48, 23, 97, 36, 27, 72, 48, 41, 58
 The only repeated number is 48, so this must
be the mode!

EX

Find the mode:
 4,
9, 2, 5, 10, 7, 1, 8, 3, 6
 Since
no number is repeated, there is no mode
Find the mode or modes, if any:
420, 360, 398, 196, 398, 400
A.) 420
B.) 398
C.) 360
D.) 400 and 298 are both modes
E.) No mode
5 NUMBER SUMMARY
The 5 number summary describes the
minimum, the maximum, Q1, the median (or
Q2), and Q3
 What is all this Q stuff?

QUARTILES

When I say Q1, I mean Quartile 1
 What
does quartile sound like?
 Quarter-
when we split up a data set into 4 parts, we
have 4 quarters. The separating number is call the
quartile.
Q2 is the median of the set
 Q1 is the median of the 1st half of the set
 Q3 is the median of the 2nd half of the set

HERE’S HOW IT WORKS
Given the set 4, 9, 2, 5, 10, 7, 1, 8, 3, 6
 The first step is to write them in order
 The next step is to find the median, This is Q2


Because it falls between 2 numbers, the median
is the average of 5 and 6.
Next find the median of each side of the
median
 Identify the min and max
 Lastly list the minimum, Q1, Q2,Q3, and the
maximum to get the 5 number summary
 1, 3, 5.5, 8, 10

Q2
MIN Q1
Q3 MAX
5.5
1 2 3 4 5 |6 7 8 9 10
Find the 5 number summary for the
set:
420, 360, 398, 196, 398, 400
196, 360, 398, 398, 400, 420
A.) 420, 398, 398, 360 196
B.) 196,360, 398, 398, 400
C.) 420, 400, 398, 196
D.) 196, 360, 398, 400, 420
E.) 196, 420
WHAT DO WE DO WITH THE 5 NUMBER
SUMMARY?






Box and whisker plot
Take the set of data from the last example, and look at
the 5 number summary:
1, 3, 5.5, 8, 10
On a number line, plot these 5 numbers
Draw a box around Q1 and Q3
Draw a line through Q2
Draw lines connecting the min to Q1 and the max to Q3
MIN
Q1
Q2
Q3
MAX
MEASURE OF DISPERSION
Also called range
 It is the difference between the minimum and
the maximum. (always positive!)

 In
our set of data the min was 1 and the max was
10
 The difference is 10-1=9, so our range is 9
INTERQUARTILE RANGE
IQR
 The difference between Q3 and Q1
 In our set 3 was Q1 and 8 was Q3, so the
IQR=8-3=5
 This will always be a positive number!!

Find the range of the data set:
420, 360, 398, 196, 398, 400
A.) 224
B.) 200
C.) 400
D.) 196
E.) 38
Find the IQR for the following data
set:
420, 360, 398, 196, 398, 400
A.) 420
B.) 40
C.) 38
D.) 224
E.) 196

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