L1 · Shapes of Distributions: Symmetric, Uniform, Skewed

Learning goal

“I can describe the shape of a distribution - symmetric, uniform, or skewed left or right - from a dot plot, bar graph or histogram described in words, and I can say how many peaks it has. I know the skew is named for its tail, and that changing a histogram's interval size can change the shape I see.”

Distribution — a whole data set together with how often each value occurs. Its pattern can be drawn as a dot plot, a bar graph, or a histogram.

Symmetric — a distribution whose left and right sides are mirror images around the centre.

Uniform — a distribution where every value (or interval) occurs about equally often: the bars are all about the same height, with no peak.

Skewed — a distribution with a long tail on one side. Skewed right: the tail stretches toward the high values. Skewed left: the tail stretches toward the low values. The skew is named for the TAIL, not for where the data piles up.

Worked example

A dot plot shows quiz scores out of 80 for 10 students. The dots stack like this: score 60: 1 dot; 65: 2 dots; 70: 4 dots; 75: 2 dots; 80: 1 dot. Step 1: Read the heights left to right: 1, 2, 4, 2, 1. Step 2: The stacks climb to one peak at 70, then come down in the same pattern - the right side mirrors the left side around 70. Step 3: Name it: this distribution is symmetric, with one peak (unimodal). Say it plainly: shape is read from the PATTERN of the heights. A mirror pattern is symmetric; equal heights are uniform; a pile with a long tail on one side is skewed - and the name follows the tail.

Check yourself — explain it

Why is the dot plot above called symmetric?

Paired problem — example still visible

Books read last month, 12 students. Dots: 0 books: 2; 1 book: 2; 2 books: 2; 3 books: 2; 4 books: 2; 5 books: 2. Name the shape. -> Uniform - every stack is the same height (2), so there is no peak and no tail.

Faded completion — last step is yours

"Waiting times at a clinic (minutes). Dots: 2 min: 4; 3 min: 3; 4 min: 2; 5 min: 1; 14 min: 1. Most dots are piled at the ___ values, and a long ___ stretches toward the high values, so the shape is skewed ___." -> low; tail; right

Ready to practise?

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

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