Unit 1.2 – Descriptive Statistics
Standard Deviation
Degrees of Freedom
Variance
68-95-99.7 Rule
Data Types
Individuals
Categorical
Quantitative
Bar Graphs
Pie Charts
Stem Plots
Histograms
Graphing Categorical Variables
Graphing Quantitative Variables
Dot Plots
Unit 1.2 – Descriptive Statistics
Part 1
Standard Deviation
Degrees of Freedom
Variance
68-95-99.7 Rule
Unit 1 – Descriptive Statistics
Our data set on temperature readings has been modified using a
transformation and is shown below:
70.2
77.4
74.7
90.9
104.4
81.9
85.5
86.4
86.4
75.6
74.7
68.4
94.5
84.6
81.9
The most commonly used measure of spread in AP Statistics is
standard deviation. Find both the variance and standard deviation for
the data set above. Make sure you understand the relationship
between variance and standard deviation.
The degrees of freedom is simply n – 1 where n is the sample size. We
will use n and n – 1 very often throughout the year.
Unit 1 – Descriptive Statistics
70.2
77.4
74.7
90.9
104.4
81.9
85.5
86.4
86.4
75.6
74.7
68.4
94.5
84.6
81.9
Understanding the 68-95-99.7 Rule
Often times we will talk about
a data point or observation
with respect to the mean and
standard deviation.
Ex 1.
Mean = 82.5
Standard Deviation = 9.577
Unit 1 – Descriptive Statistics
70.2
77.4
74.7
90.9
104.4
81.9
85.5
86.4
86.4
75.6
74.7
68.4
94.5
84.6
81.9
Ex 1.
Mean = 82.5
Standard Deviation = 9.577
There is a major assumption being made when using the 68-95 Rule and that is
that the data is normally distributed.
We will talk more about this idea in Unit 1.3 but for now, know that this means
the distribution is spread about the mean proportionally to it’s standard
deviation. In otherwords N(x,s)
Unit 1 – Descriptive Statistics
70.2
77.4
74.7
90.9
104.4
81.9
85.5
86.4
86.4
75.6
74.7
68.4
94.5
84.6
81.9
Ex 1.
Mean = 82.5
Standard Deviation = 9.577
Checking for Understanding…
1. What percent of days can we expect to have a temperature lower than 53.769˚ F?
2. What percent of days can we expect to have a temperature lower than 72.923˚ F?
3. What percent of days can we expect to have a temperature lower than 82.5˚ F?
4. What percent of days can we expect to have a temperature lower than 101.654˚ F?
Unit 1 – Descriptive Statistics
70.2
77.4
74.7
90.9
104.4
81.9
85.5
86.4
86.4
75.6
74.7
68.4
94.5
84.6
81.9
Ex 1.
Mean = 82.5
Standard Deviation = 9.577
Checking for Understanding…
continued…
1. What percent of days can we expect to have a temperature higher than 63.346˚ F?
2. What percent of days can we expect to have a temperature higher than 72.923˚ F?
3. What percent of days can we expect to have a temperature higher than 82.5˚ F?
4. What percent of days can we expect to have a temperature higher than 92.077˚ F?
Unit 1 – Descriptive Statistics
70.2
77.4
74.7
90.9
104.4
81.9
85.5
86.4
86.4
75.6
74.7
68.4
94.5
84.6
81.9
Ex 1.
Mean = 82.5
Standard Deviation = 9.577
Checking for Understanding…
continued…
1. What percent of days can we expect to have a temperature between 72.923˚ F and 92.077˚ F ?
2. What percent of days can we expect to have a temperature between 53.769˚ F and 111.231˚ F ?
3. What percent of days can we expect to have a temperature between 63.346˚ F and 92.077˚ F ?
4. What percent of days can we expect to have a temperature between 92.077˚ F and 111.231˚ F ?
Unit 1.2 – Descriptive Statistics
Part 2
Data Types
Individuals
Categorical
Quantitative
Unit 1.2 – Descriptive Statistics
Our next task was to gather more detailed data over a one week
period. Our data is shown below:
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Low
63
66
58
59
60
63
64
High
78
88
90
92
97
96
98
Humidity
45%
13%
10%
8%
18%
15%
8%
Precipitation Air Quality
Light
Good
No
Fair
No
Poor
No
Poor
No
Fair
No
Fair
No
Poor
Unit 1.2 – Descriptive Statistics
Day
Monday
Low
63
High
78
Humidity
45%
Precipitation Air Quality
Light
Good
Tuesday
Wednesday
Thursday
66
58
59
88
90
92
13%
10%
8%
No
No
No
Fair
Poor
Poor
Friday
Saturday
Sunday
60
63
64
97
96
98
18%
15%
8%
No
No
No
Fair
Fair
Poor
1. Identify the individuals and categories
Unit 1.2 – Descriptive Statistics
Day
Monday
Low
63
High
78
Humidity
45%
Precipitation Air Quality
Light
Good
Tuesday
Wednesday
Thursday
66
58
59
88
90
92
13%
10%
8%
No
No
No
Fair
Poor
Poor
Friday
Saturday
Sunday
60
63
64
97
96
98
18%
15%
8%
No
No
No
Fair
Fair
Poor
2. Classify each category as categorical or quantitative
Unit 1.2 – Descriptive Statistics
Day
Monday
Low
63
High
78
Humidity
45%
Precipitation Air Quality
Light
Good
Tuesday
Wednesday
Thursday
66
58
59
88
90
92
13%
10%
8%
No
No
No
Fair
Poor
Poor
Friday
Saturday
Sunday
60
63
64
97
96
98
18%
15%
8%
No
No
No
Fair
Fair
Poor
4. For each column, identify the most appropriate graphing
type
Unit 1.2 – Descriptive Statistics
Day
Monday
Low
63
High
78
Humidity
45%
Tuesday
Wednesday
Thursday
66
58
59
88
90
92
13%
10%
8%
No
No
No
Fair
Poor
Poor
Friday
Saturday
Sunday
60
63
64
97
96
98
18%
15%
8%
No
No
No
Fair
Fair
Poor
Ticket out the Door
Precipitation Air Quality
Light
Good
5. Come up with your own example of a data set that
includes all 4 vocab words and check with Mr. Newton
Unit 1.2 – Descriptive Statistics
Part 3
Graphing Categorical Variables
Bar Graphs
Pie Charts
Graphing Quantitative Variables
Dot Plots
Stem Plots
Histograms
Unit 1.2 – Descriptive Statistics
Categorical Data - Bar Graph
Unit 1.2 – Descriptive Statistics
Categorical Data – Pie Chart
Unit 1.2 – Descriptive Statistics
Quantitative Data – Dot Plot
Unit 1.2 – Descriptive Statistics
Quantitative Data – Stem and Leaf Plot
Unit 1.2 – Descriptive Statistics
Quantitative Data – Histogram
Unit 1.2 – Descriptive Statistics
Quantitative Data – Histogram