MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
STATISTICS
The study of the collection, analysis, interpretation,
presentation and organization of data.
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
STATISTICS
The study of the collection, analysis, interpretation,
presentation and organization of data.
DATA
Data is a set a values of quantitative or qualitative variables.
For purposes of what we will study here,
let’s just think of data as a set of numerical information.
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
Often information that we need to analyze
is not easy to deal with in its raw form.
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
Often information that we need to analyze
is not easy to deal with in its raw form.
One way of organizing discrete data into a more useful format is a
FREQUENCY TABLE
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
Often information that we need to analyze
is not easy to deal with in its raw form.
One way of organizing discrete data into a more useful format is a
FREQUENCY TABLE
Let’s use construct a frequency table for the data above.
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
A frequency table organizes the
data by counting the number of
occurrences (the frequency) of
each possible outcome.
EVALUATION
FREQUENCY
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
A frequency table organizes the There are
4
data by counting the number of
‘Excellent’
occurrences (the frequency) of
each possible outcome.
EVALUATION
FREQUENCY
E
4
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
A frequency table organizes the
data by counting the number of
occurrences (the frequency) of
each possible outcome.
There are
7 ‘Above
Average’
EVALUATION
FREQUENCY
E
4
7
A
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
A frequency table organizes the
data by counting the number of
occurrences (the frequency) of
each possible outcome.
There are
8
‘Average’
EVALUATION
FREQUENCY
E
4
7
8
A
V
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
A frequency table organizes the
data by counting the number of
occurrences (the frequency) of
each possible outcome.
There are
4 ‘Below
Average’
EVALUATION
FREQUENCY
E
4
7
8
4
A
V
B
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
A frequency table organizes the
data by counting the number of
occurrences (the frequency) of
each possible outcome.
There are
2
‘Poor’
EVALUATION
FREQUENCY
E
4
7
8
4
2
A
V
B
P
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
A frequency table organizes the
data by counting the number of
occurrences (the frequency) of
each possible outcome.
There are
25
in all
EVALUATION
FREQUENCY
E
4
7
8
4
2
25
A
V
B
P
TOTAL
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
This is the
frequency table
for the data
above.
EVALUATION
FREQUENCY
E
4
7
8
4
2
25
A
V
B
P
TOTAL
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
If we take a
frequency
table
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
If we take a
frequency
table
…and replace counts
with probabilities,
we get a RELATIVE
FREQUENCY table.
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
If we take a
frequency
table
…and replace counts
with probabilities,
we get a RELATIVE
FREQUENCY table.
EVALUATION
E
A
V
B
P
TOTAL
PROBABILITY
4
25
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
If we take a
frequency
table
…and replace counts
with probabilities,
we get a RELATIVE
FREQUENCY table.
EVALUATION
E
A
V
B
P
TOTAL
PROBABILITY
4
25
7
25
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
If we take a
frequency
table
…and replace counts
with probabilities,
we get a RELATIVE
FREQUENCY table.
EVALUATION
E
A
V
B
P
TOTAL
PROBABILITY
4
25
7
25
8
25
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
If we take a
frequency
table
…and replace counts
with probabilities,
we get a RELATIVE
FREQUENCY table.
EVALUATION
E
A
V
B
P
TOTAL
PROBABILITY
4
25
7
25
8
25
4
25
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
If we take a
frequency
table
…and replace counts
with probabilities,
we get a RELATIVE
FREQUENCY table.
EVALUATION
E
A
V
B
P
TOTAL
PROBABILITY
4
25
7
25
8
25
4
25
2
25
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
If we take a
frequency
table
…and replace counts
with probabilities,
we get a RELATIVE
FREQUENCY table.
EVALUATION
E
A
V
B
P
TOTAL
PROBABILITY
4
25
7
25
8
25
4
25
2
25
1
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the Often
latest episode
of CSI. column
the ‘Probability’
The possible evaluations are
will(B)elow
be labeled
‘Relative
(E)xcellent, (A)bove average, a(V)erage,
average,
(P)oor
Frequency’.
After the show, the 25 evaluations were
as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
If we take a
frequency
table
…and replace counts
with probabilities,
we get a RELATIVE
FREQUENCY table.
EVALUATION RELATIVE FREQUENCY
4
E
25
7
A
25
8
V
25
4
B
25
2
P
25
TOTAL
1
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
We will begin by looking at ways to organize data.
25 viewers evaluated the latest episode of CSI.
The possible evaluations are
(E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor
After the show, the 25 evaluations were as follows:
A V V B P E A E V V A E P B V V A A A E B V A B V
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
If we take a
frequency
table
…and replace counts
with probabilities,
we get a RELATIVE
FREQUENCY table.
EVALUATION RELATIVE FREQUENCY
4
E
25
7
A
25
8
V
25
4
B
25
2
P
25
TOTAL
1
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
Let’s construct a frequency table using equal sized intervals starting ’50-54’.
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
Let’s construct a frequency table using equal sized intervals starting ’50-54’.
SCORES
FREQUENCY
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
Let’s construct a frequency table using equal sized intervals starting ’50-54’.
SCORES
50 - 54
FREQUENCY
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
Let’s construct a frequency table using equal sized intervals starting ’50-54’.
SCORES
50 - 54
FREQUENCY
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
Let’s construct a frequency table using equal sized intervals starting ’50-54’.
SCORES
50 - 54
FREQUENCY
2
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
Let’s construct a frequency table using equal sized intervals starting ’50-54’.
SCORES
50 - 54
55 - 59
FREQUENCY
2
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
Let’s construct a frequency table using equal sized intervals starting ’50-54’.
SCORES
50 - 54
55 - 59
FREQUENCY
2
4
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
Let’s construct a frequency table using equal sized intervals starting ’50-54’.
SCORES
50 - 54
55 - 59
60 - 64
FREQUENCY
2
4
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
Let’s construct a frequency table using equal sized intervals starting ’50-54’.
SCORES
50 - 54
55 - 59
60 - 64
FREQUENCY
2
4
6
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
Let’s construct a frequency table using equal sized intervals starting ’50-54’.
SCORES
50 - 54
55 - 59
60 - 64
65 - 69
FREQUENCY
2
4
6
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
Let’s construct a frequency table using equal sized intervals starting ’50-54’.
SCORES
50 - 54
55 - 59
60 - 64
65 - 69
FREQUENCY
2
4
6
8
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
Let’s construct a frequency table using equal sized intervals starting ’50-54’.
SCORES
50 - 54
55 - 59
60 - 64
65 - 69
FREQUENCY
2
4
6
8
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
Let’s construct a frequency table using equal sized intervals starting ’50-54’.
SCORES
50 - 54
55 - 59
60 - 64
65 - 69
TOTAL
FREQUENCY
2
4
6
8
20
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
If Let’s
you want
construct
a relative
a frequency
frequency
table
table
using
instead,
equal just
sizeddivide
intervals
eachstarting
frequency
’50-54’.
by 20.
SCORES
50 - 54
55 - 59
60 - 64
65 - 69
TOTAL
RELATIVE FREQUENCY
2
4
6
8
20
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
If Let’s
you want
construct
a relative
a frequency
frequency
table
table
using
instead,
equal just
sizeddivide
intervals
eachstarting
frequency
’50-54’.
by 20.
SCORES
50 - 54
55 - 59
60 - 64
65 - 69
TOTAL
RELATIVE FREQUENCY
2/20
4/20
6/20
8/20
20
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
If Let’s
you want
construct
a relative
a frequency
frequency
table
table
using
instead,
equal just
sizeddivide
intervals
eachstarting
frequency
’50-54’.
by 20.
SCORES
50 - 54
55 - 59
60 - 64
65 - 69
TOTAL
RELATIVE FREQUENCY
2/20
4/20
6/20
8/20
20
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Sometimes there are so many different outcomes that a frequency or
relative frequency table is not useful without grouping the data.
20 health care workers take an assessment with these scores:
62
59
53
58
67
56
68
64
61
67
51
68
66
57
66
65
64
69
61
60
If Let’s
you want
construct
a relative
a frequency
frequency
table
table
using
instead,
equal just
sizeddivide
intervals
eachstarting
frequency
’50-54’.
by 20.
SCORES
50 - 54
55 - 59
60 - 64
65 - 69
TOTAL
RELATIVE FREQUENCY
1/10
1/5
3/10
2/5
20
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
If we prefer, we can turn a frequency or relative frequency table into a
BAR GRAPH.
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
If we prefer, we can turn a frequency or relative frequency table into a
BAR GRAPH.
Let’s turn the frequency
table we constructed earlier
into a BAR GRAPH.
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
FREQUENCY
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
If we prefer, we can turn a frequency or relative frequency table into a
BAR GRAPH.
Let’s turn the frequency
table we constructed earlier
10
into a BAR GRAPH.
8
6
4
2
Let’s put the
frequencies on the
vertical axis.
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
FREQUENCY
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
If we prefer, we can turn a frequency or relative frequency table into a
BAR GRAPH.
Let’s turn the frequency
table we constructed earlier
10
into a BAR GRAPH.
8
6
4
2
…and the outcomes
on the horizontal axis.
E
A
V
B
P
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
FREQUENCY
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
If we prefer, we can turn a frequency or relative frequency table into a
BAR GRAPH.
Finally, let the height of
Let’s turn the frequency
each bar represent the
table we constructed earlier
10
corresponding frequency.
into a BAR GRAPH.
8
6
4
2
E
A
V
B
P
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
FREQUENCY
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
If we prefer, we can turn a frequency or relative frequency table into a
BAR GRAPH.
Finally, let the height of
Let’s turn the frequency
each bar represent the
table we constructed earlier
10
corresponding frequency.
into a BAR GRAPH.
8
6
4
2
E
A
V
B
P
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
FREQUENCY
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
If we prefer, we can turn a frequency or relative frequency table into a
BAR GRAPH.
Finally, let the height of
Let’s turn the frequency
each bar represent the
table we constructed earlier
10
corresponding frequency.
into a BAR GRAPH.
8
6
4
2
E
A
V
B
P
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
FREQUENCY
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
If we prefer, we can turn a frequency or relative frequency table into a
BAR GRAPH.
Finally, let the height of
Let’s turn the frequency
each bar represent the
table we constructed earlier
10
corresponding frequency.
into a BAR GRAPH.
8
6
4
2
E
A
V
B
P
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
FREQUENCY
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
If we prefer, we can turn a frequency or relative frequency table into a
BAR GRAPH.
Finally, let the height of
Let’s turn the frequency
each bar represent the
table we constructed earlier
10
corresponding frequency.
into a BAR GRAPH.
8
6
4
2
E
A
V
B
P
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
FREQUENCY
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
If we prefer, we can turn a frequency or relative frequency table into a
BAR GRAPH.
Finally, let the height of
Let’s turn the frequency
each bar represent the
table we constructed earlier
10
corresponding frequency.
into a BAR GRAPH.
8
6
4
2
E
A
V
B
P
EVALUATION FREQUENCY
E
A
V
B
P
TOTAL
4
7
8
4
2
25
FREQUENCY
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
If we prefer, we can turn a frequency or relative frequency table into a
BAR GRAPH.
Let’s turn the frequency
table we constructed earlier
10
into a BAR GRAPH.
8
6
4
2
E
A
V
B
P
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
If the data from a frequency or relative frequency table is continuous
rather than discrete, we construct the ‘bars’ with no space between
them and call the resulting graph a histogram instead of a bar graph.
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
If the data from a frequency or relative frequency table is continuous
rather than discrete, we construct the ‘bars’ with no space between
them and call the resulting graph a histogram instead of a bar graph.
We will not be focusing on the difference between discrete
and continuous here. If you simply think of ‘discrete values’ as
values that are completely distinct from each other and
‘continuous values’ as values that can sort of bleed over into
each other, you will be OK for what we will be doing.
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
If the data from a frequency or relative frequency table is continuous
rather than discrete, we construct the ‘bars’ with no space between
them and call the resulting graph a histogram instead of a bar graph.
We will not be focusing on the difference between discrete
and continuous here. If you simply think of ‘discrete values’ as
values that are completely distinct from each other and
‘continuous values’ as values that can sort of bleed over into
each other, you will be OK for what we will be doing.
A quick example to help with this distinction:
If you are counting things, the counts are discrete.
There is no doubt that 2 is different than 3.
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
If the data from a frequency or relative frequency table is continuous
rather than discrete, we construct the ‘bars’ with no space between
them and call the resulting graph a histogram instead of a bar graph.
We will not be focusing on the difference between discrete
and continuous here. If you simply think of ‘discrete values’ as
values that are completely distinct from each other and
‘continuous values’ as values that can sort of bleed over into
each other, you will be OK for what we will be doing.
A quick example to help with this distinction:
If you are counting things, the counts are discrete.
There is no doubt that 2 is different than 3.
But if you are measuring a person’s height, one person might measure and get
59.99 inches while another person might measure the same person and get
60.01 inches. (In this sense, the values sort of bleed into each other.)
MATH 110 Sec
14-1worry
Lecture:
Statistics-Organizing
and Visualizing Data
Don’t
if this
distinction is not perfectly
clear
to you. Itor
really
will not
have much
If the data from
a frequency
relative
frequency
tableifis continuous
any impact
on whatthe
we ‘bars’
are doing
rather than discrete,
we construct
withhere.
no space between
them and call the resulting graph a histogram instead of a bar graph.
We will not be focusing on the difference between discrete
and continuous here. If you simply think of ‘discrete values’ as
values that are completely distinct from each other and
‘continuous values’ as values that can sort of bleed over into
each other, you will be OK for what we will be doing.
A quick example to help with this distinction:
If you are counting things, the counts are discrete.
There is no doubt that 2 is different than 3.
But if you are measuring a person’s height, one person might measure and get
59.99 inches while another person might measure the same person and get
60.01 inches. (In this sense, the values sort of bleed into each other.)
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Let’s construct a histogram from the frequency table below.
Pounds lost
0 to 10
10+ to 20
20+ to 30
30+ to 40
Total
Frequency
14
23
17
11
65
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Let’s construct a histogram from the frequency table below.
Frequency
14
23
17
11
65
FREQUENCY
Pounds lost
0 to 10
10+ to 20
20+ to 30
30+ to 40
Total
25
20
15
10
5
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Let’s construct a histogram from the frequency table below.
Frequency
14
23
17
11
65
FREQUENCY
Pounds lost
0 to 10
10+ to 20
20+ to 30
30+ to 40
Total
25
20
15
10
5
0 to 10 10+ to 20 20+ to 30 30+ to 40
Pounds Lost
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Let’s construct a histogram from the frequency table below.
Frequency
14
23
17
11
65
FREQUENCY
Pounds lost
0 to 10
10+ to 20
20+ to 30
30+ to 40
Total
25
20
15
10
5
0 to 10 10+ to 20 20+ to 30 30+ to 40
Pounds Lost
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Let’s construct a histogram from the frequency table below.
Frequency
14
23
17
11
65
FREQUENCY
Pounds lost
0 to 10
10+ to 20
20+ to 30
30+ to 40
Total
25
20
15
10
5
0 to 10 10+ to 20 20+ to 30 30+ to 40
Pounds Lost
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Let’s construct a histogram from the frequency table below.
Frequency
14
23
17
11
65
FREQUENCY
Pounds lost
0 to 10
10+ to 20
20+ to 30
30+ to 40
Total
25
20
15
10
5
0 to 10 10+ to 20 20+ to 30 30+ to 40
Pounds Lost
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Let’s construct a histogram from the frequency table below.
Frequency
14
23
17
11
65
FREQUENCY
Pounds lost
0 to 10
10+ to 20
20+ to 30
30+ to 40
Total
25
20
15
10
5
0 to 10 10+ to 20 20+ to 30 30+ to 40
Pounds Lost
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
Let’s construct a histogram from the frequency table below.
Frequency
14
23
17
11
65
FREQUENCY
Pounds lost
0 to 10
10+ to 20
20+ to 30
30+ to 40
Total
25
20
15
10
5
0 to 10 10+ to 20 20+ to 30 30+ to 40
Pounds Lost
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
A Stem-and-Leaf plot is another visual way to display data.
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
A Stem-and-Leaf plot is another visual way to display data.
In constructing a stem-and-leaf display, we view each number as having
two parts. The left digit is considered the stem and the right digit the
leaf. This is probably best illustrated through an example.
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
These are the number of home runs hit by the home run champions in
the National League for the years 1975 to 1989 and for 1993 to 2007.
1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47
1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50
Compare these home run records using a stem-and-leaf display.
MATH
110
Sec 14-1
Statistics-Organizing
and Visualizing Data
The left
(BLUE)
digit Lecture:
is considered
the stem
These are the number of home runs hit by the home run champions in
the National League for the years 1975 to 1989 and for 1993 to 2007.
1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47
1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50
Compare these home run records using a stem-and-leaf display.
MATH
110
Sec 14-1
Statistics-Organizing
and Visualizing Data
The left
(BLUE)
digit Lecture:
is considered
the stem
These are the number of home runs hit by the home run champions in
and
(RED)
digit
considered
leaf.to 2007.
the National League
forthe
theright
years
1975
tois1989
and forthe
1993
1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47
1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50
Compare these home run records using a stem-and-leaf display.
MATH
110
Sec 14-1
Statistics-Organizing
and Visualizing Data
The left
(BLUE)
digit Lecture:
is considered
the stem
These are the number of home runs hit by the home run champions in
and
(RED)
digit
considered
leaf.to 2007.
the National League
forthe
theright
years
1975
tois1989
and forthe
1993
1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47
1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50
Compare these home run records using a stem-and-leaf display.
1975–1989
MATH
110
Sec 14-1
Statistics-Organizing
and Visualizing Data
The left
(BLUE)
digit Lecture:
is considered
the stem
These are the number of home runs hit by the home run champions in
and
(RED)
digit
considered
leaf.to 2007.
the National League
forthe
theright
years
1975
tois1989
and forthe
1993
1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47
Among the46,
left43,
(blue)
are 50,
only73,
threes,
fours
and
1993–2007:
40, digits,
47, 49,there
70, 65,
49, 47,
48,
51,fives.
58, 50
Compare these home run records using a stem-and-leaf display.
1975–1989
MATH
110
Sec 14-1
Statistics-Organizing
and Visualizing Data
The left
(BLUE)
digit Lecture:
is considered
the stem
These are the number of home runs hit by the home run champions in
and
(RED)
digit
considered
leaf.to 2007.
the National League
forthe
theright
years
1975
tois1989
and forthe
1993
1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47
Among the46,
left43,
(blue)
are 50,
only73,
threes,
fours
and
1993–2007:
40, digits,
47, 49,there
70, 65,
49, 47,
48,
51,fives.
58, 50
Compare these home run records using a stem-and-leaf display.
1975–1989
For the leaves, write down each
rightmost (red) digit in numerical order
next to the stem that it belongs to.
MATH
110
Sec 14-1
Statistics-Organizing
and Visualizing Data
The left
(BLUE)
digit Lecture:
is considered
the stem
These are the number of home runs hit by the home run champions in
and
(RED)
digit
considered
leaf.to 2007.
the National League
forthe
theright
years
1975
tois1989
and forthe
1993
1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47
1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50
Compare these home run records using a stem-and-leaf display.
1975–1989
MATH
110
Sec 14-1
Statistics-Organizing
and Visualizing Data
The left
(BLUE)
digit Lecture:
is considered
the stem
These are the number of home runs hit by the home run champions in
and
(RED)
digit
considered
leaf.to 2007.
the National League
forthe
theright
years
1975
tois1989
and forthe
1993
1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47
1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50
Compare these home run records using a stem-and-leaf display.
1975–1989
1993–2007
MATH
110
Sec 14-1
Statistics-Organizing
and Visualizing Data
The left
(BLUE)
digit Lecture:
is considered
the stem
These are the number of home runs hit by the home run champions in
and
(RED)
digit
considered
leaf.to 2007.
the National League
forthe
theright
years
1975
tois1989
and forthe
1993
Among the left
digits,
are31,
only
fours,
fives,37,
sixes
1975–1989:
38,(blue)
38, 52,
40,there
48, 48,
37,
40, 36,
37,and
49,sevens.
39, 47
1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50
Compare these home run records using a stem-and-leaf display.
1975–1989
1993–2007
MATH
110
Sec 14-1
Statistics-Organizing
and Visualizing Data
The left
(BLUE)
digit Lecture:
is considered
the stem
These are the number of home runs hit by the home run champions in
and
(RED)
digit
considered
leaf.to 2007.
the National League
forthe
theright
years
1975
tois1989
and forthe
1993
Among the left
digits,
are31,
only
fours,
fives,37,
sixes
1975–1989:
38,(blue)
38, 52,
40,there
48, 48,
37,
40, 36,
37,and
49,sevens.
39, 47
1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50
Compare these home run records using a stem-and-leaf display.
1975–1989
For the leaves, write down each
1993–2007
rightmost (red) digit
in numerical order
next to the stem that it belongs to.
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
These are the number of home runs hit by the home run champions in
the National League for the years 1975 to 1989 and for 1993 to 2007.
1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47
1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50
Compare these home run records using a stem-and-leaf display.
1975–1989
1993–2007
MATH
110
Sec 14-1
Lecture:
Statistics-Organizing
and Visualizing
Data
We
canleft
compare
these
data by
placing
the two displays
side by side.
The
(BLUE)
digit
is considered
the stem
These
the number
home runs hit
by the home plot.
run champions in
Someare
people
call this aofBack-to-back
Stem-and-Leaf
and
(RED)
digit
considered
leaf.to 2007.
the National League
forthe
theright
years
1975
tois1989
and forthe
1993
1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47
1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50
Compare these home run records using a stem-and-leaf display.
1975–1989
1993–2007
MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data
In summary, these are the data organization and display methods discussed
FREQUENCY TABLE
BAR GRAPH
RELATIVE FREQUENCY TABLE
HISTOGRAM
STEM-AND-LEAF PLOT/DISPLAY