The document explains how to create histograms to visualize the results of a geometry test and cappuccino coffee production at a café. It details the process of grouping numerical data into class intervals to reduce the number of bars in the histogram and provides examples of class widths for different amounts of bars. The final histogram displays frequency data for cappuccino production over two days using grouped classes.

1. Geometry Test Results
Image Source: http://johnpatrickserrano.blogspot.com.au

2. In any Histogram, people need a simple and easy
to read graph, which has between 5 and 10 bars.
(This can be done by using “Class Intervals” or “Bins”).
Geometry Test Results The Geometry Test Results histogram
would be far too big if we charted
each of the 30 or so result scores on a
separate bar for each score.
We have created a graph which is
smaller and manageable, (with only 6
bars instead of 30 or more).
Image Source: http://johnpatrickserrano.blogspot.com.au

3. “Class Intervals”, “Class Width”, “Classes”, “Bar Width” and
“Bins” all refer to the idea of grouping numerical data into
equal width groups. We can then count how many of our
items belong in each group.
The Geometry Test Results histogram
contains “Groups of 10” :
Geometry Test Results
50 – 60 which is scores from 50 to 59
60 – 70 which is scores from 60 to 69
and so on.
Use your fingers to count:
50, 51, 52, 53, 54, 55, 56, 57, 58, 59
Image Source: http://johnpatrickserrano.blogspot.com.au
is a group of TEN .
( eg. 50 to 59 is more than nine items! ).

4. The following data relates to how many Cappuccino
Coffees were made at a Café every hour during
two full working days.
4, 9, 9, 11, 3, 9, 10, 17, 12,
6, 18, 0, 5, 11, 9, 12, 11, 15
First we rewrite the numbers from lowest to highest:
0, 3, 4, 5, 6, 9, 9, 9, 9, 10, 11, 11, 11, 12, 12, 15, 17, 18
We have 12 different number values, but ten different
values is the maximum for a Histogram containing 10 bars.
So we need to do grouping into “Classes” to reduce this.

5. Cappuccino Coffees made at a Café every hour:
0, 3, 4, 5, 6, 9, 9, 9, 9, 10, 11, 11, 11, 12, 12, 15, 17, 18
For a Histogram containing 10 bars:
Class Width = (Highest Item – Lowest Item) ÷ 10
= (18 – 0) ÷ 10
= 1.8 which rounds off to 2 .
Image Source: http://cutestfood.com
The ten Classes of width size 2 we need are :
0-1, 2-3, 4-5, 6-7, 8-9, 10-11, 12-13, 14-15, 16-17, 18-19

6. Cappuccino Coffees made at a Café every hour:
0, 3, 4, 5, 6, 9, 9, 9, 9, 10, 11, 11, 11, 12, 12, 15, 17, 18
For a Histogram containing 5 bars:
Class Width = (Highest Item – Lowest Item) ÷ 5
= (18 – 0) ÷ 5
= 3.6 which rounds off to 4 .
The five Classes of width size 4 we need are :
0-3, 4-7, 8-11, 12-15, 16-19 (remember to count on fingers)
Image Source: http://blogspot.com

7. Cappuccino Coffees made at a Café every hour:
0, 3, 4, 5, 6, 9, 9, 9, 9, 10, 11, 11, 11, 12, 12, 15, 17, 18
For a Histogram containing 5 bars, we need these classes:
0-3, 4-7, 8-11, 12-15, 16-19
We can count our items into these groups to make the following:
Number of Cups
Tally Frequency
of Cappuccino
0-3 // 2
4-7 /// 3
8 - 11 //// /// 8
12 - 15 /// 3
16 - 19 // 2 Image Source: http://www.espressospot.com

8. We now use our five class Frequency Table to create a
Histogram graph of the Cappuccino Coffee Statistics.
Number of
Freq
Cappuccinos
0-3 2 8
4-7 3
6
8 – 11 8
12 - 15 3 4
16 - 19 2
2
0
0–3
Number of Cappuccinos Made Per Hour
Image Source: http://www.blogspot.com

9. http://passyworldofmathematics.com/