Random articles
Fractions Intro Time, Subtraction and 24 Hour Clock Functions Introduction Long Division Volume of a Pyramid Combinations without Repetition Sketching Quadratic GraphsOnce certain data or statistics have been recorded and collected, there then needs to be suitable
methods to display such data.
One of the most common and simplest methods of displaying data is with a Frequency Table, or an
additional Cumulative Frequency Table.
Frequency means the numbers of times a value occurs.
An example of collecting some simple data is asking a group of  20 people how many books
they have read in a year.
Let's say the results came back as the list of numbers below.
This data can be displayed in an appropriate table.
Books Read  Tally  Frequency 
1  
2  
3  
4  
5  
6  
Total 
In the table there is a column for the number of books read, the tally marks , and the frequency, which is the
results of the tally marks.
The horizontal rows represent each data value possible when the group are asked how many books they
read.
Now below is the filled in frequency table with the groups answers to books read from the list
above.
Books Read  Tally  Frequency 
1   

2   

3 


4   

5 


6   

Total 

In the books read example above, we only had to deal with data values between 1 and
6.
But often there can be cases where there is a much broader range of values to present.
Say we had a list of the number of customers at a restaurant over a 2 week period,
14 different days.
Shown in the list below.
There are  14 different data values listed, a different number of customers for each day.
As opposed to the books read example, were there were only  6 different values returned
from a group of  20 people.
We don't really want to have  14 separate horizontal rows for each different number of
customers over the  2 weeks.
Instead, we can do something that is called "grouping data".
Where we split the set of values up into intervals.
This list of data values we have for restaurant customers range from 46 up to 102.
102 − 46 = 56
Let's look to split this large interval range up into smaller intervals, of equal size.
We'll aim for  6 intervals. \bf{\frac{56}{6}}
= 9.33
We now want to round 9.33 to a whole number, but unlike with usual rounding where we can
round up and down.
We actually always round up when creating groups for grouping data in frequency tables.
9.33 rounds up to 10.
So each interval in the table will each cover 10 data values.
We can start  Group 1 at 45, Group 2 at 55 and so on.
Number of Customers  Tally  Frequency 
45  54  
55  64  
65  74  
75  84  
85  94  
95  104  
Total 
This table can be filled in the same way as before, with a tally mark for each customer number within the correct given interval group.
Number of Customers  Tally  Frequency 
45  54   

55  64   

65  74   

75  84   

85  94   

95  104   

Total 

A cumulative frequency table is slightly different from a standard frequency table.
This is when we add a third column to the table, where we keep a running total of data values at
each stage, adding up each frequency.
We can show this with the original books read table from the beginning of this page.
Books Read  Frequency  Cumulative Frequency 
1  4  4 
2  2  6 (4+2) 
3  6  12 (6+6) 
4  1  13 (12+1) 
5  5  18 (13+5) 
6  1  20 (18+2) 
Total  20 
A cumulative frequency table can be useful if you want to know how many values are more than or less
than a certain level.
For example the table above tells us that there were 13 people who read 4 books or
less in a year.