Download Measures of Center and Spread

Homework Questions
Measures of
Center and Spread
Unit 5, Statistics
Mean
The mean is more commonly known as
the average.
Represented by x
A six-month study of a busy intersection
reports that the number of accidents per
month as 3, 8, 5, 6, 6, 10. Find the mean.
Example 2
 In the real estate section of the Sunday paper,
the following house prices were listed. Find the
mean.
$98,000
$136,700
$210,000
$289,900
$315,500
$2,456,500
Median
If the distribution is skewed, or contains
extreme values, often the median is the
best measure of center.
It is the middle value of your data.
3, 4, 7, 8, 9, 11, 15
17, 22, 24, 30, 35, 40
Go back to home prices and find the
median instead of the mean…
$98,000
$136,700
$210,000
$289,900
$315,500
$2,456,500
Mode
The mode is the data value that has the
highest frequency, which means it occurs
the most often in the list of data.
NOTE: if every value in the data occurs
the same number of times there is no
mode. If two or more repeat the same
number of times the set is bimodal (2
values), trimodal (3 values), or multimodal.
Find the mode
Recall the shapes…
For a symmetric distribution, the mean
and median are equal
Recall the shapes…
For a distribution skewed to the right, the
mean is to the right of the median
Recall the shapes…
For a distribution skewed to the left, the
mean is to the left of the median.
Standard Deviation
I am not going to teach you how to find
this by hand, but you do need to know
what it is…
The Standard Deviation is the most
common measure of variability (the spread
of the data) and is best used when data is
symmetric.
It measures the average distance of a
piece of data to the mean.
CALCULATOR TIME!!
 Type this into L1 on
your calc and find:
 x=
 Med =
 Mode =
 Standard Deviation =
Your turn…
85, 91, 99, 101, 105, 109, 111, 119, 125

=
Med =
Mode =
Standard Deviation =
x
Range
The range is the difference between the
maximum and minimum data values.
85, 91, 99, 101, 105, 109, 111, 119, 125
Range is 125 – 85 = 40
Interquartile Range
Example: 5, 8, 4, 4, 6, 3, 8
Put them in order: 3, 4, 4, 5, 6, 8, 8
Half way is the Q2
Half of the 1st half is Q1
Half of the 2nd half is Q3
IQR = Q3 - Q1
Find the IQR and the 5 Number Summary
Five Number Summary –
Minimum, Q1, Median, Q3, Maximum
1, 3, 3, 4, 5, 6, 6, 7, 8, 8
Box Plot
You can use the 5 Number Summary to
create a box plot of the data.
Your turn…
Find the 5 number summary, IQR, and
create a box plot of the data
85, 91, 99, 101, 105, 109, 111, 119, 125
Homework
Section 13.2 Worksheet