7 7 Statistics Statistical Graphs

							7.7 Statistics & Statistical
          Graphs
           p.445
      An intro to Statistics

• Statistics – numerical values used to
  summarize & compare sets of data (such
  as ERA in baseball).

• Measures of Central Tendency – mean,
  median, & mode are the 3 we will be
  using. Tells you what the “center” of the
  data is.
Mean – ( x ) average of n numbers
 (add all #s & divide by n)
Median – the middle # when the #s are
 written in order from least to greatest
 or greatest to least. If there are 2
 middle numbers, the median will be
 the average of those 2.
Mode – the number(s) that occur most
 frequently. It is possible to have more
 than 1 mode or even no mode.
  Ex: Find the mean, median, & mode of
 the following set of numbers: 36, 39, 40,
    34, 48, 33, 25, 30, 37, 17, 42, 40, 24.
• Mean -     445
                   34.2
             13
Median – Put the numbers in order first!
17, 24, 25, 30, 33, 34, 36, 37, 39, 40, 40, 42, 48

Mode – most frequent!
                40 is the mode.
    Measures of Dispersion – tell how
    spread out the data are.
         * Range – Difference between the
    largest and smallest values.
       (for example: the range of the last
    example would be 48-17=31)
            * Standard Deviation - (σ – “sigma”)
          ( x1  x) 2  ( x2  x) 2  ... ( xn  x) 2 x is the mean
  
                               n                      x1, x2, x3, …, xn
                                                      are the entries in
n is the number of entries in the set                 the data set.
     Ex: Find the standard deviation of the data
               from the first example.
   (36  34.2) 2  (39  34.2) 2  (40  34.2) 2  ... (24  34.2) 2

                                  13

                            856 .32
                         
                              13
                           65 .87
                            8.12
             Box-and-whisker plots
        Whisker                         Box          Whisker


   0         10       20           30         40        50



Minimum
value (17)                                                   Maximum
                                        Median               value (48)
              Lower Quartile –           (36)
                median of all                       Upper Quartile –
             numbers in the list                 median of all numbers
              to the left of the                   to the right of the
                   median                               median
              (25+30)/2 = 27.5                       (40+40)/2 = 40
       Hints for making a
     box-and-whiskers plot:
• Make sure data is in order from least to
  greatest.
• Find the minimum value, median,
  maximum value, upper & lower quartiles.
• Plot the points for this info below a number
  line.
• Draw the box and whiskers.
         Frequency Distribution
Assign appropriate                          Count the
                       Put a tally mark   number of tally
 intervals that will
                        for each data     marks and put
  include all data       value in the
 values in the set.                       the total in the
                       appropriate row.    last column.

                       Title Goes Here
       Interval            Tally       Frequency
        0 to 9                             0
       10 to 19                 l          1
       20 to 29                ll          2
       30 to 39             llll l         6
       40 to 49               llll         4
    Another way to show the same
       info. is in a histogram.
    Frequency
                 TITLE HERE   Bars should be
L
A                               touching!
B
     6
E    5
L    4
     3
H
     2
E    1
R    0
E
                                    Intervals
                LABEL HERE
Assignment