# 7 7 Statistics Statistical Graphs

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```							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
* 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

```
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