Building a Frequency Table

In a meeting the other day, the presenter was talking about a range of different failures for the product in question. She talked about each issue, a bit about the failure analysis, yet didn’t reveal which failures occurred more or less often.

She did provide a handout with a listing of the problems in order of the product field age and listing of the failure name (component or system involved). So, I grabbed a piece of paper to create a frequency table so I could quickly determine which problems occurred more often than others.

A Frequency Table Defintion

A frequency table tabulates the number of times (a count, tally or frequency) a bit of data occurs in a dataset.

These tables work for continuous and discreet data and for a smaller dataset are quickly constructed by hand. (it was a rather boring meeting, too).

Steps to Construct a Frequency Table

1. Starting with a dataset, scan the data for the minimum and maximum values if numbers. These become the range over which to tally the values. Else, identify the unique values.
2. List the unique data values (or bins of values) suitable for counting the occurrence of those values within the dataset.
3. Tally or count the data values into the table.

That’s it. No ordering, sorting, calculating (other than counting).

Building a Frequency Table Step by Step

Let’s imagine the meeting mentioned above was about failures within computer system. The issues reported were catalogued into the major subsystems of the computer: screen, keyboard, motherboard, hard drive, and power supply. The data also included the number of weeks since the computer was manufactured.

Here’s the data (or just the first page of reported issues)

Issue	Subsystem	Weeks
1	Power Supply	5
2	Mother board	6
3	Mother board	6
4	Power Supply	7
5	Screen	7
6	Mother board	8
7	Hard drive	8
8	Hard Drive	8
9	Power Supply	9
10	Power Supply	10
11	Hard drive	11
12	Hard drive	11
13	Hard drive	11
14	Mother board	11
15	Hard drive	12
16	Hard drive	12

To set up the table for the subsystems, we would just list the subsystems as they are unique elements of the system.

Subsystem	Count
Screen
Keyboard
Motherboard
Hard drive
Power supply

Then run through the dataset and count the occurrence of each item. I mark the item to indicate it’s been counted.

Subsystem	Count
Screen	1
Keyboard	0
Motherboard	4
Hard drive	7
Power supply	4

A quick check on counting everything, is to sum the counts in the table and it should equal the number of listed items in the dataset. In this case we have 16 records and the sum of counts in the table is also 16.

A frequency table for the age at failure starts with a scan of the data to identify the minimum and maximum values. Here the minimum weeks is 5 and maximum is 12. Thus we can set up a table that runs from 5 through 12 in steps of 1.

Weeks	Count
5	1
6	2
7	2
8	3
9	1
10	1
11	4
12	2

Then run through the dataset and count the number of occurrences of 5 weeks, then 6 weeks, and so on.

Summary

A frequency table is a versatile and practical means to summarize data quickly. There are ways to do this in your favorite spreadsheet of using a statistical package, yet sometimes opening your laptop, inputting the data, formatting, etc. just takes too long. With a small dataset, it’s just quicker to grab a piece of paper.

The table provides insights on most and least often occurring elements of the data along with other bits of information that may be useful. The process to create a table is easier than creating Pareto Chart of Histogram. It works with any kind of data and does not require any manipulation or calculations other than counting.

The next time you’re in a meeting and jumble of data, grab a piece of paper and let a simple frequency table help you make sense of the dataset.

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