Transcript Frequency Distributions

Frequency Distributions
And Histograms

Frequency = count of how many times an
observation occurs in a set of data

Distribution = pattern of frequencies of an
observation

Histogram = a type of graph used to
display a frequency distribution

Grouped data = put into classes and
organized
◦ (i.e. 1 5 4 3 2 2 5)

Ungrouped = big list of numbers that
hasn’t been put in categories yet
◦ i.e
Value
Frequency
1
1
2
2
3
1
4
1
5
2
Example 1: How many times does Maddy
get bored in a day???
 This data is recorded from 20 days of
observation, and how many times of
boredom in a day is shown:

◦ 1, 4, 3, 1, 1, 3, 0, 3, 3, 0,
◦ 0, 5, 3, 2, 2, 5, 5, 0, 5, 3

This is ungrouped data – each number is
an observation because we observe how
many times she is bored on that day

Step 1: Put your data in numerical order
0, 0, 0, 0, 1, 1, 1, 2, 2, 3,
 3, 3, 3, 3, 3, 4, 5, 5, 5, 5


This helps make grouping data easier

Step 2: Make a chart of your data

This data is now grouped

Step 3: Define your classes

Sometimes the problem will give you the
number of classes it wants in a histogram,
in this case, it doesn’t

Now we use our judgment to decide the
size of our classes

In this case, it’s easy to make each class
cover 1 observation. For example, the first
class covers 0 times of boredom up until,
but not including 1. In other words, the
first class covers the observations where
she was bored 0 times in a day

Notice how I wrote the frequencies of
each observation next to its class

For example, on 4 different days Maddy
was bored 0 times , so the frequency you
write in the table from
is 4

Step 4: Make your histogram

Draw axis that so that your x-axis is your
classes and the y-axis is your frequency

So…your x-axis should cover 0 to 6 and
your y-axis should cover 0 to 6 as well. If
you want, you can make your axis bigger
as long as you keep your graph accurate
when you draw it

To make the graph, think of a bar graph
with the bars connected to each other on
the sides instead of having spaces

Here is your histogram:

Notice the bars have the same width so no
bar looks unnaturally wide and they are
connected to each other on the sides

Remember: histograms can only be made
if your classes in the frequency chart are
numerical, like how many times Maddy is
bored in a day or how many red M & M’s
are in 20 packs you open

If you get something like how many of
each color are in a single pack of M & M’s,
you can still make a frequency chart, but
you can’t make a histogram, because your
data will be categorical
This is a chart of colors and how many appeared in a bag of M&M’s
Color
Frequency
Red
4
Blue
7
Yellow
2
Green
5
Brown
5
Orange
8
Notice how you could make a bar graph out of the data, but a
Histogram wouldn’t work because the classes are categorical
And not numerical