L2.5: Describing Categorical Data - Mode and Median

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Learning outcomes

• define mode and median
• identify when mode can be used for categorical data
• identify when median may be used for ordinal data
• avoid invalid summaries for nominal categories

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Mode

• The mode is the most frequent category or value.
• For categorical data, mode is often the most meaningful central summary.

• blood group responses -> mode = most common blood group
• favourite sport -> mode = most commonly chosen sport

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Median

• The median is the middle value when observations are arranged in order.
• Median needs an order.

• nominal categories -> no median
• ordinal categories -> median may be meaningful

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Why median is not valid for nominal data

• Nominal categories have no natural order.
• Without order, there is no “middle” category.

• blood group categories cannot be arranged meaningfully as a statistical order

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Median for ordinal data

• satisfaction levels: low, medium, high
• class performance groups: poor, average, good, excellent

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Mode vs median in categorical context

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Exam hints and traps

• If categories are unordered, median is invalid.
• Mode is valid for both nominal and ordinal categorical data.
• Mean is generally not meaningful for pure categorical labels.
• Ordered labels are not enough for mean, but they may allow median.

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Quick practice

1. Can blood group have a mode?
2. Can blood group have a median?
3. Can satisfaction level (low, medium, high) have a median?
4. Which measure is safest for nominal categories?

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Answer key

1. Yes
2. No
3. Yes
4. Mode