Mean_ Median_ Mode_ 5 number Summary_ and Center of Dispersion

Document Sample
Mean_ Median_ Mode_ 5 number Summary_ and Center of Dispersion Powered By Docstoc
					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?
     Wenormally 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   5.5  Q3 MAX
     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!)
     Inour 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

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:0
posted:4/2/2013
language:English
pages:23