11.1 Find Measures of
Central Tendency &
Dispersion
Algebra II
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. 1: 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
the data set.
n is the number of entries in the set
Ex 2: Find the standard deviation of the
data from the first example. 36, 39, 40, 34,
48, 33, 25, 30, 37, 17, 42, 40, 24.
(36  34.2) 2  (39  34.2) 2  (40  34.2) 2  ...  (24  34.2) 2

13
856.32

13
  65.87
  8.12
assignment
•
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
• 17, 24, 25, 30, 33, 34, 36, 37, 39, 40, 40, 42, 48
• Plot the points for this info below a number
line.
• Draw the box and whiskers.
Box-and-whisker plots
Box
Whisker
0
10
20
30
Minimum
value (17)
Lower Quartile –
median of all
numbers in the list
to the left of the
median
(25+30)/2 = 27.5
Whisker
40
Median
(36)
50
Maximum
value (48)
Upper Quartile –
median of all numbers
to the right of the
median
(40+40)/2 = 40
Frequency Distribution
Assign appropriate
intervals that will
include all data
values in the set.
Interval
0 to 9
10 to 19
20 to 29
30 to 39
40 to 49
Put a tally mark
for each data
value in the
appropriate row.
Count the
number of tally
marks and put
the total in the
last column.
Title Goes Here
Tally
Frequency
0
l
1
ll
2
llll l
6
llll
4
Another way to show the same
info. is in a histogram.
Frequency
L
A
B
E
L
H
E
R
E
TITLE HERE
Bars should be
touching!
6
5
4
3
2
1
0
Intervals
LABEL HERE
Assignment