Frequency Distributions
A frequency distribution divides a data set into classes and
makes a table based on the frequencies in each class.
Frequency Distributions
A frequency distribution divides a data set into classes and
makes a table based on the frequencies in each class.
Here, for example, are the number of hits in twenty at-bats for
thirty baseball players:
Hits
Frequency
0−2
4
3−5
13
6−8
10
9 − 11
2
12 − 14
1
Frequency Distributions
0, 3, 6, 9, and 12 are the lower class limits
Frequency Distributions
0, 3, 6, 9, and 12 are the lower class limits
2, 5, 8, 11, and 14 are the upper class limits
Frequency Distributions
0, 3, 6, 9, and 12 are the lower class limits
2, 5, 8, 11, and 14 are the upper class limits
1, 4, 7, 10, and 13 are the class midpoints
Frequency Distributions
0, 3, 6, 9, and 12 are the lower class limits
2, 5, 8, 11, and 14 are the upper class limits
1, 4, 7, 10, and 13 are the class midpoints
The class boundaries are 2.5, 5.5, 8.5,etc.
Frequency Distributions
0, 3, 6, 9, and 12 are the lower class limits
2, 5, 8, 11, and 14 are the upper class limits
1, 4, 7, 10, and 13 are the class midpoints
The class boundaries are 2.5, 5.5, 8.5,etc.
The frequencies record the number of cases in each class interval.
They add to n, the number of scores (Here n = 30).
Frequency Distributions
0, 3, 6, 9, and 12 are the lower class limits
2, 5, 8, 11, and 14 are the upper class limits
1, 4, 7, 10, and 13 are the class midpoints
The class boundaries are 2.5, 5.5, 8.5,etc.
The frequencies record the number of cases in each class interval.
They add to n, the number of scores (Here n = 30).
For continuous data often :
Frequency Distributions
0, 3, 6, 9, and 12 are the lower class limits
2, 5, 8, 11, and 14 are the upper class limits
1, 4, 7, 10, and 13 are the class midpoints
The class boundaries are 2.5, 5.5, 8.5,etc.
The frequencies record the number of cases in each class interval.
They add to n, the number of scores (Here n = 30).
For continuous data often :
upper class limit = class boundary = next lower class limit
Frequency Distributions
0, 3, 6, 9, and 12 are the lower class limits
2, 5, 8, 11, and 14 are the upper class limits
1, 4, 7, 10, and 13 are the class midpoints
The class boundaries are 2.5, 5.5, 8.5,etc.
The frequencies record the number of cases in each class interval.
They add to n, the number of scores (Here n = 30).
For continuous data often :
upper class limit = class boundary = next lower class limit
When this is the case the lower endpoint convention is used for
boundary scores.
Relative Frequency Distributions
A relative frequency distribution uses percents (fractions,
decimals), i.e. relative frequencies, in place of frequencies. For the
ball players:
Relative Frequency Distributions
A relative frequency distribution uses percents (fractions,
decimals), i.e. relative frequencies, in place of frequencies. For the
ball players:
Hits
Rel.Freq.
0−2
0.13
3−5
0.43
6−8
0.3
9 − 11
0.06
12 − 14
0.03
Relative Frequency Distributions
A relative frequency distribution uses percents (fractions,
decimals), i.e. relative frequencies, in place of frequencies. For the
ball players:
Hits
Rel.Freq.
0−2
0.13
3−5
0.43
6−8
0.3
9 − 11
0.06
12 − 14
0.03
These relative frequencies must add to 1 (100%).
Relative Frequency Distributions
A relative frequency distribution uses percents (fractions,
decimals), i.e. relative frequencies, in place of frequencies. For the
ball players:
Hits
Rel.Freq.
0−2
0.13
3−5
0.43
6−8
0.3
9 − 11
0.06
12 − 14
0.03
These relative frequencies must add to 1 (100%).
Note: It is not required that class intervals are all the same length.
Cumulative Frequency Distributions
A cumulative frequency distribution gives the sum of the
observations in each class and all preceding classes. Again the ball
players:
Cumulative Frequency Distributions
A cumulative frequency distribution gives the sum of the
observations in each class and all preceding classes. Again the ball
players:
Hits
Cumul.Freq.
0−2
4
3−5
17
6−8
27
9 − 11
29
12 − 14
30
The Histogram
A histogram is a graphical version of a frequency or relative
frequency histogram.
The Histogram
A histogram is a graphical version of a frequency or relative
frequency histogram.
The horizontal axis contains the scores, divided into class
intervals.
The Histogram
A histogram is a graphical version of a frequency or relative
frequency histogram.
The horizontal axis contains the scores, divided into class
intervals.
Over each interval is a bar area of which represents the
proportion of cases on that interval.
The Histogram
A histogram is a graphical version of a frequency or relative
frequency histogram.
The horizontal axis contains the scores, divided into class
intervals.
Over each interval is a bar area of which represents the
proportion of cases on that interval.
If all classes are of equal length, can use either absolute or relative
frequency for the height of the bar; the resulting picture is
essentially the same.
The Histogram
A histogram is a graphical version of a frequency or relative
frequency histogram.
The horizontal axis contains the scores, divided into class
intervals.
Over each interval is a bar area of which represents the
proportion of cases on that interval.
If all classes are of equal length, can use either absolute or relative
frequency for the height of the bar; the resulting picture is
essentially the same.
With unequal class intervals, we must use density scale for the
vertical axis.
The Histogram
Consider making a histogram from this frequency distribution of
annual salaries (K$) for forty employees of a small company:
The Histogram
Consider making a histogram from this frequency distribution of
annual salaries (K$) for forty employees of a small company:
Salary(K$) Freq.
0 − 20
4
20 − 40
17
40 − 60
12
60 − 100
5
100 − 200
2
The Histogram
Consider making a histogram from this frequency distribution of
annual salaries (K$) for forty employees of a small company:
Salary(K$) Freq.
0 − 20
4
20 − 40
17
40 − 60
12
60 − 100
5
100 − 200
2
Observe that to obtain a representative histogram, we must use
density for the vertical scale.
Other Graphical Displays
Other Graphical Displays
For nominal data there are:
Other Graphical Displays
For nominal data there are:
I
Pie Charts
Other Graphical Displays
For nominal data there are:
I
Pie Charts
I
Bar Graphs
Other Graphical Displays
For nominal data there are:
I
Pie Charts
I
Bar Graphs
I
Pareto Charts
Other Graphical Displays
For nominal data there are:
I
Pie Charts
I
Bar Graphs
I
Pareto Charts
For small quantitative data sets:
Other Graphical Displays
For nominal data there are:
I
Pie Charts
I
Bar Graphs
I
Pareto Charts
For small quantitative data sets:
I
Dotplots
Other Graphical Displays
For nominal data there are:
I
Pie Charts
I
Bar Graphs
I
Pareto Charts
For small quantitative data sets:
I
Dotplots
I
Stem-and-Leaf Plots
Other Graphical Displays
For nominal data there are:
I
Pie Charts
I
Bar Graphs
I
Pareto Charts
For small quantitative data sets:
I
Dotplots
I
Stem-and-Leaf Plots