Measures of Central Tendency

• What is the middle of the data.
• This is a number, that tells us about all of the data
• More specifically, what is the middle of the data. (Or average)
• There is no one good way to do this, it depends on what you want to know.
• Mean
  • Σx/n
  • Add up all the numbers and divide by the number of numbers.
• Example: problem 2, page 702

      data: 11, 6, 4, 0, 2, 1, 12, 0, 0
      n = 9
      mean = (11+6+4+0+2+1+12+0+0) / 9 = 36/9 = 4
      

• Example: Problem 10

  n =  31
  Mean = (1*2+2*4+3*5+4*7+5*6+6*4+7*3)/31
       = 127/31 = 4.1
      

• The Median is the middle data item.
  • arrange the data low to high.
  • If there is an odd number of data, the median is the middle number
  • If there is an even number of data, the median is the average of the two middle numbers.
  • The median is at position (n+1)/2
• Example: 14

  0 0 0 1 2 4 6 11 12
  There are 9 data items, so the median is at position 5
  The median is 2
      

• Example: 16

  30 70 90 100 100 100
  n = 6
  median is average of 3 and 4
     = (90 + 100)/ 2 = 95
      

• Example 22

  there are 31 data items, so the median is at
      (31+1)/2 = 16
  This will be one of the 7 4s.
      

• The Mode is the data item that occurs most frequently.
• If more than one data item occurs most frequently, then each is the mode.
• Example: 26

  0 occurs three times, so it is the mode.
      

• Example: 34

  4 occurs most times so it is the mode.
      

• The midrange of the data is (low data value + high data value)/2
• Example: 38

  low = 0
  high = 11
  (0+11)/2 =  5.5
      

• Example: 46

  (1+7)/2 = 4
      

• How would you do number 50?
• How would you do number 54?

Homework