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Tally and Frequency Table


When we collect and record data, we want to have a suitable method to display the data and findings.


A common and straightforward method of displaying standard data is with a ‘Frequency Table’, or with an additional ‘Cumulative Frequency Table’.

Frequency refers to the number of times a value occurs.

This page will show how to construct and make use of a tally and frequency table.




Frequency Table

An example of collecting and recording some data could be asking a group of  20  people how many films they have watched in a month.

The results of films watched could come back as the list of numbers below.

{ 1 , 3 , 4 , 2 , 6 , 5 , 4 , 2 , 1 , 5 , 3 , 3 , 3 , 1 , 7 , 3 , 2 , 3 , 5 , 4 }



This collected data can be displayed in an appropriate tally and frequency table, shown below.

Films Watched  Tally  Frequency
1
2
3
4
5
6
7
Total

In this table there is a column for the number of films watched, the tally marks of each number, and the frequency, which is the total of the relevant tally marks.

The horizontal rows of the table represent each data value possible when the group are asked how many films they watched.




Below now is the filled in completed frequency table, with the groups answers to films watched from the list of numbers above.

Films Watched  Tally  Frequency
1 |||
3
2 |||
3
3 |||| |
6
4 |||
3
5 |||
3
6 |
1
7 |
1
Total
20




Frequency Tables and Grouping Data


With the films watched example above, we just had to deal with data values that were between  1  and  7.

However there can often be situations when there is a broader range of values to record and display.


Say we had a list of the number of shirts sold at a clothes shop over a  2  week period, so  14  different days.

The shirt sales on the  14  days are as follows.

{ 48 , 104 , 87 , 73 , 56 , 61 , 67 , 51 , 58 , 99 , 78 , 85 , 49 , 63 }

There are  14  different data values listed, a different of shirts sold for each day of the two weeks.


As opposed to the films watched example, were there were just  7  different values returned from a group of  20  people.
With this larger set of values, we perhaps don’t really want to have  14  horizontal rows for each different number of shirts sold over the  2  weeks.

Instead, we can do what is called  “grouping data”.
Which is when we split the set of data values we have up into intervals.




Grouping Data

The list of data values for the shirts sold range from  48  up to  104.

104 − 48 = 56


We’ll look to divide this large interval range up into some smaller intervals, which will be of equal size.
Let’s aim for  6  smaller intervals.

Dividing the range by  6  will tell us how large each smaller interval should be.     \bf{\frac{56}{6}}  =  9.33

We now want to round  9.33  to a whole number, but unlike with standard rounding where we can round up and down when required.
Here we always round up when creating intervals for grouping data in frequency tables.

So  9.33  is rounded up to  10.

Thus each interval in our table will each cover a range of  10  data values.


The first interval doesn’t strictly have to start with the lowest data value. we could start group one at  46,  group two at  55  and so on.

Number of Shirts Sold Tally Frequency
46 – 55
56 – 65
66 – 75
76 – 85
86 – 95
96 – 105
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.

{ 48 , 104 , 87 , 73 , 56 , 61 , 67 , 51 , 58 , 99 , 78 , 85 , 49 , 63 }


Number of Customers Tally Frequency
46 – 55 |||
3
56 – 65 ||||
4
66 – 75 ||
2
76 – 85 ||
2
86 – 95 |
1
96 – 105 ||
2
Total
14




Tally and Frequency Table,
Cumulative Frequency Table


A cumulative frequency table is a little bit different from the standard frequency tables seen so far.


This table is when we add an extra third column, where we keep a running total of the data values at each interval stage, summing up each frequency.

We can create a cumulative frequency table with the original films watched table from the beginning of the page.

Films Watched  Tally  Frequency
1
2
3
4
5
6
7
Total

In this table there is a column for the number of films watched, the tally marks of each number, and the frequency, which is the total of the relevant tally marks.
The horizontal rows of the table represent each data value possible when the group are asked how many films they watched.


Below now is the filled in completed frequency table, with the groups answers to films watched from the list of numbers above.

Films Watched  Frequency  Cumulative Frequency
1 3
3
2 3
6 (3+3)
3 6
12 (6+6)
4 3
15 (12+3)
5 3
18 (15+3)
6 1
19 (18+1)
7 1
20 (19+1)
Total 20

A cumulative frequency table can at times be useful if you wish to know how many data values are more than or less than a certain number.

For example the cumulative frequency table above tells us that there were  15  people who watched  4  films or less in a month.





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