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Understanding Categorical Data

When you ask your friends what their favourite chocolate bar is, you cannot calculate a mathematical "average" chocolate bar. This type of information is known as qualitative data, which describes a quality or characteristic and is usually expressed in words (like car makes or favourite colours).

When this data is divided into distinct, non-overlapping groups where each piece of data belongs to exactly one group, it is called categorical data. While mostly qualitative, categorical data can occasionally be numerical if the numbers act purely as labels, such as bus route numbers or phone models. Because you cannot calculate a meaningful mean for this type of data, the mode (the most frequent category) is the only average that can be used.

Constructing Frequency Tables from Raw Data

Before you can draw a chart, you need to organise your raw data (data in its original, unorganised form) into a frequency table. A frequency table summarises large data sets by showing the frequency, which is the total count of how many times a specific category occurs.

When constructing a table from raw data, a tally system acts as an essential intermediate step to ensure no data point is missed.

Worked Example: Constructing a Frequency Table

A survey asked 20 students for their favourite sport. The raw data is: Football, Netball, Football, Rugby, Netball, Football, Football, Netball, Rugby, Football, Netball, Tennis, Football, Football, Netball, Rugby, Netball, Football, Tennis, Netball.

Step 1: List the distinct categories in the first column.

Step 2: Go through the raw data one by one and record a tally using "five-bar gate" notation (four vertical lines and a diagonal fifth).

Step 3: Count the tallies to find the frequency () for each category.

Method	Frequency ( $f$ )	Calculation ( $f \times 6^\circ$ )	Sector Angle
Car	18	$18 \times 6^\circ$	$108^\circ$
Bus	12	$12 \times 6^\circ$	$72^\circ$
Walk	23	$23 \times 6^\circ$	$138^\circ$
Bike	7	$7 \times 6^\circ$	$42^\circ$
Total	60		$360^\circ$

Students often misinterpret a quarter symbol in a pictogram as automatically representing '1 unit'. You must always divide the key value by 4 (e.g., if the key is 12, a quarter symbol is 3).

In AQA exams, it is mandatory to leave equal gaps between bars in a bar chart for categorical data; failing to do so will lose you construction marks.

When calculating pie chart angles, if your angles do not sum to exactly 360°, you have made a calculation error and should immediately recheck your multiplier.

When tallying raw data, draw a single line through each value in the original list as you record it to ensure you do not miscount or skip any data points.

If a pie chart question states 'Not to Scale', do not attempt to measure the angles with a protractor; you must use calculation or ratio methods to find the missing frequencies.

Data describing a quality or characteristic, typically expressed in words and impossible to measure numerically.

Data divided into non-overlapping groups where each piece of data belongs to exactly one category.

The most frequent value or category in a data set; the only average suitable for categorical or qualitative data.

Data in its original, unorganised form exactly as it was collected.

A table used to summarise large sets of data, displaying categories alongside their corresponding tallies and frequencies.

The total number of times a specific data value or category occurs.

A system of recording data occurrences using marks, typically grouped in fives (four vertical lines and a diagonal fifth).

A visual representation of data where frequency is represented by the proportional number of symbols.

A crucial guide accompanying a pictogram or chart that defines the numerical value or meaning of specific symbols, colours, or patterns.

A visual representation using equal-width bars where the height or length is proportional to the frequency, separated by equal gaps for categorical data.

The central angle in a pie chart representing a category's proportional slice of the total 360 degrees.

The number of degrees representing one unit of frequency in a pie chart, found by calculating 360 divided by the total frequency.