L2 · Choosing the most appropriate measure

Learning goal

“I can choose the most appropriate measure of central tendency for a situation - mode for categories and most-common values, median when an extreme value would drag the mean, and mean when the values are fairly even - and I can say why.”

Central tendency — a single value that describes the centre or "typical" part of a data set: mean, median or mode.

Typical value — the value that honestly represents most of the data.

Category data — data that names kinds, not amounts: favourite colour, shoe size sold, type of pet. You cannot add categories, so the mean and median do not work for them.

Extreme value — one value that is far above or far below the rest of the data.

Worked example

A shoe store recorded the sizes it sold one day: 7, 8, 8, 9, 8, 10, 8. Step 1: The store's question is "which size should we stock the most of?" That is a most-often question. Step 2: Mode = 8 (sold 4 times). The mean is 58 / 7, about 8.3 - the store cannot stock a size "8.3," and 8.3 is not even the size that sold most. Step 3: For category data - favourite colour, kind of pet, size to stock - the mode is the most appropriate measure, often the only one that makes sense. Model both ways: a tally chart of the sizes sold, AND the mode card held up beside the mean card so the two summaries can be compared directly. Say it plainly: match the measure to the question. "Most common?" -> mode.

Check yourself — explain it

Why is the mode the best measure for the shoe store?

Paired problem — example still visible

A class voted for favourite fruit: apple 9 votes, banana 4, orange 6, grape 4. Which measure describes the class's favourite, and what is it? -> Mode: apple (9 votes). The data is categories, so mean and median do not apply.

Faded completion — last step is yours

"A pet survey found: dogs 12, cats 10, fish 3, birds 2. The most appropriate measure is the ___ , which is ___." -> mode; dogs

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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