Warm-Up

3
4
6
10
15
55



To become president of the United States, a candidate does not
have to receive a majority of the popular vote. The candidate does
have to win a majority of the 538 electoral votes that are cast in
the Electoral College. Here are the number of electoral votes for
each of the 50 states and the District of Columbia.
3
4
7
10
15
3
4
7
10
15
3
5
7
10
17
3
5
7
11
20
3
5
8
11
21
3
5
8
11
21
Make a step and leaf plot for the data
Make a box and whisker plot for the data
Describe the distribution
3
5
9
11
27
4
6
9
12
31
4
6
9
13
34
Homework Questions
Quiz 1st!
…then Section 1.3 Continued
Numerical Summaries of Distributions
Use 3 flights from our planes
Find your mean/average
 Find your range
 Instead of measuring spread by range…we
need a better measure of spread…
 Find the average distance away from the
mean for your data set
 Pair up and discuss how you might do that
 Problem solve on what goes wrong, if
anything, and ways you can fix it

Let’s Discuss…

What went wrong?

What are some possible solutions to that
problem?

Why are we finding the average distance
from the mean?
Standard Deviation
Variance is the average squared distance
from the mean.
 Standard Deviation is the average
distance, so you 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒

To find Standard Deviation
Find the distance of each observation
from the mean
 Square each of those distances
 Average that by dividing the sum by n-1

◦ This = variance
 Sx
is the square root of this average
Example
Here are the foot lengths (in cm) for a
random sample of 14 year olds.
 25, 22, 20, 25, 24, 24, 28
 Mean =

x
25
22
20
25
24
24
28
A few notes…
You should use standard deviation when
you used the mean for the measure of
center
 Sx is always greater than or equal to 0.
 Sx = 0 only when there is no variability (all
values have the same value)
 As the observations become more spread
out about their mean, sx gets larger
 It has the same measurements as the
original observation.

Homework

Pg 72 (97-110 all)