DESCRIPTIVE STATISTICS
Frequency Distributions and Their
Graphs
Frequency Distribution
 Def: a table that shows classes or intervals of
the data entries with a count of the number of
entries in each class, f.
 Frequency Distributions may also include:
 - Cumulative frequencies, cf. (running total)
 - Relative frequencies, rf. (% of total)
 - Class Midpoint (aka Class Mark) (sum of
class limits, divided by 2)
 Find (a) class width, (b) class midpoints, and (c)
class boundaries
 Travel time to work (in minutes)
Class
Frequency, f
0–9
10 – 19
20 – 29
30 – 39
40 – 49
50 – 59
60 – 69
188
372
264
205
83
76
32
Construct a Frequency Distribution:
1. Decide on the # of classes to include (between 5
and 20)
2. Find the class width: range of the data divided
by the # of classes, round UP if needed.
3. Find the class limits: These are the lower and
upper values for each class. Classes cannot
overlap!
4. Tally the data to find the frequency, f, for each
class.
Construct a cumulative
frequency distribution:
 Daily saturated fat intakes (in grams) for a sample of
people:
38
54
57
24
32
32
40
42
34
17
25
16
39
29
36
31
40
33
33
33
Graphs of frequency distributions:
 Frequency Histogram: a bar graph that represents
the distribution.
 1. Horizontal scale = classes
 2. Vertical scale = frequencies of classes
 3. Consecutive bars touch - Use class
BOUNDARIES on the horizontal scale.
 Frequency Polygon: a line graph that emphasizes
the continuous change in frequencies. (Must start
and end at 0 to close the shape)
 Cumulative Frequency graph (OGIVE): a line
graph that displays the cumulative frequency of
each class at its upper boundary.
 1. Horizontal scale: first lower boundary and all
upper boundaries of the classes.
 2. Vertical scale: frequencies
 3. graph goes from 1st lower boundary (cf = 0) to
last upper boundary (cf = n)
 Relative Frequency Histogram: has the same
shape as a frequency histogram, but uses the
RELATIVE frequencies on the vertical axis.