Stats
Pop Quiz
1) True or False?
2) Up or Down?
3) Left or Right?
4) Potatoes or French Fries?
5) Coke or Pepsi?
6) Summer or Winter?
7) Justin Bieber or Selena Gomez?
8) Red or Green?
9) Day or Night?
10) Giraffe or Monkey?
Grade Your Quiz
1) True
2) Down
3) Right
4) French Fries
5) Pepsi
6) Summer
7) Justin Bieber
8) Green
9) Day
10) Monkey
Measures of Central Tendency
• Mean: sum of data values/number of data
values
• Median: middle value or mean of two middle
values
• Mode: most frequently occurring value
Now let’s find the mean, median, and mode of your quiz scores.
Outlier
• A value that is substantially different from
other data in the set.
• Which is an outlier in the set of values?
– 32, 25, 87, 39, 19, 36, 18
Quartile
One of three values that divides a set of data into four parts.
This data shows water temperatures of the ocean in Pensacola, Florida.
Now let’s find the lower quartile and upper quartile of your quiz scores.
Box Plot
Method of displaying data that uses quartiles to form the
center box and the minimum and maximum values to
form “whiskers”.
Now let’s make a box plot of your quiz scores.
Range
The difference between the highest and lowest data values.
86 – 56 = 30 The range is 30.
Now let’s find the range of your quiz scores.
Interquartile Range
The difference between the first and third quartiles.
83 – 60.5 = 22.5 The interquartile range is 30.
Now let’s find the interquartile range of your quiz scores.
Your Turn
• You surveyed 9 of your friends and found out their
ACT scores: 24, 19, 22, 31, 25, 24, 21, 18, 29
a. Find the mean, median, and mode of the data.
A.
Mean: 23.6; Median: 24; Mode: 24
b. Find the upper and lower quartiles of the data.
A.
Lower: 20; Upper: 27
c. Make a box plot of the data.
A.
18 20
d. What is the range of the data?
A.
13
e. What is the interquartile range of the data?
A.
7
24
27
31
Math Test Scores
Math Test Scores
Math Test Scores
Intro Activity
• For your set of data, do the following:
1. Find the mean, median, mode
2. Find the range
3. Find the lower and upper quartile
4. Find the interquartile range
Set 1 77
78
79
80
80
81
82
83
Set 2 20
60
70
80
80
90
100
140
Set 3 50
60
70
80
80
90
100
110
Set 4 20
30
40
80
80
120
130
140
Intro Activity
• Are the sets the same?
• What does the range tell you about the sets?
• Find two sets that are spread out differently, but their range is
the same.
• Find two sets that are spread out differently, but their
interquartile range is the same.
Set 1 77
78
79
80
80
81
82
83
Set 2 20
60
70
80
80
90
100
140
Set 3 50
60
70
80
80
90
100
110
Set 4 20
30
40
80
80
120
130
140
The Normal Distribution
A normal distribution of data means that most of the points in a set of data
are close to the "average," while relatively few points tend to one extreme
or the other.
Different Normal Distributions
Data spread out
Most data close to mean
Standard Deviation
• The standard deviation ( ) is a statistic that
tells you how tightly all the various examples
are clustered around the mean in a set of
data.
When the data are spread
apart and the bell curve is
more flat, that tells you you
have a relatively large
standard deviation.
When the data are pretty
tightly bunched together
and the bell-shaped curve
is steep, the standard
deviation is small.
One standard deviation
One standard deviation away
from the mean in either
direction on the horizontal
axis (the red area on the
above graph) accounts for
somewhere around 68
percent of the people in this
group.
One standard deviation
Two standard deviations
Two standard deviations
away from the mean (the red
and green areas) account for
roughly 95 percent of the
people.
Two standard deviations
Three standard deviations
Three standard deviations
(the red, green and blue
areas) account for about 99
percent of the people.
Three standard deviations
Men’s Heights
69”
Mean is 69”
Standard Deviation is 2.8
60.6”
63.4”
66.2”
71.8”
74.6”
77.4”
Men’s Heights
69”
Michael Jordan is 78” tall
60.6”
63.4”
66.2”
71.8”
74.6”
77.4”
Outlier
• A value that is substantially different from
other data in the set.
• Michael Jordan’s height is an outlier.
Women’s Heights
63.6”
Mean is 63.6”
Standard Deviation is 2.5
56.1”
58.6”
61.1”
66.1”
68.6”
71.1”
• The standard deviation of men’s heights is
2.8”
• The standard deviation of women’s heights is
2.5”
• What does this tell you about how the
distributions compare?
Example 1
• An average light bulb manufactured by the Acme Corporation
lasts 300 days with a standard deviation of 50 days.
• Sketch the normal curve for this distribution, labeling the xaxis with the values that are one, two, and three standard
deviations from the mean.
150
200
250
300
350
400
450
Example 2
• An average IQ is 100 with a standard deviation of 10.
• Sketch the normal curve for this distribution, labeling the xaxis with the values that are one, two, and three standard
deviations from the mean.
70
80
90
100
110
120
130
Example 3
Your production plant employs several seamstresses whose
production rate is a normal distribution with a mean (x) of 50
jeans per month and a standard deviation ( ) of 3 jeans.
a) About what percent of the seamstress produce between 47
and 53 jeans per month?
68%
b) What is the probability that a seamstress selected at random
will produce more than 56 jeans per month?
2.5%
c) What is the probability that a seamstress
selected at random will produce between 44
and 47 jeans per month?
13.5%
Conclusions – Lap Times
• Racer A has a mean lap time of 20 seconds,
with a standard deviation of 2.1 seconds.
• Racer B has a mean lap time of 21 seconds
with a standard deviation of 3.2 seconds.
• What can you conclude about the two racers?
Normal Curve
The mean and median
are the SAME.
Mean – balance point
Median – cuts area
under curve in half
• A football team has the following scores for
their season: 28, 39, 49, 10, 52, 0, 3, 35, 46,
38.
• Find the mean of the scores.
• The team won 7 games and lost 3 games. In
the games they lost, they scored 0, 3, and 10
points.
• Find the mean of the scores of the games they
won.
• How do the means compare?
Negatively Skewed
The low outliers pull
the mean down.
Positively Skewed
The high outliers pull
the mean up.
Positively skewed, negatively
skewed or normal?
Positively skewed, negatively
skewed or normal?
Positively skewed, negatively
skewed or normal?
Positively skewed, negatively
skewed or normal?
Positively skewed, negatively
skewed or normal?
Positively skewed, negatively
skewed or normal?
Calculating Standard Deviation
• Worksheet