L5 · Statistics Clinic

Learning goal

“I can put the whole unit together on fresh data: name a distribution's shape, choose and justify a typifying statistic, spot when a histogram's intervals are misleading, and build and read circle graphs - running the checks (percents to 100, angles to 360) every time.”

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.

Typical value — a single number that fairly represents a whole data set; the statistic you would quote to describe "how much, usually."

Sector — one slice of the circle, standing for one category.

Central angle — the angle at the centre of the circle that opens up a sector; angle = percent x 360°.

Worked example

Texts sent per day by 8 teens: 5, 8, 9, 10, 10, 11, 12, 60. Step 1: Shape: the values pile from 5 to 12 and one value trails far to the right - skewed right. Step 2: Predict before computing: right skew means the mean will be pulled ABOVE the median. Step 3: Median: average of the 4th and 5th values = (10 + 10) / 2 = 10. Mean: sum = 125; 125 / 8 = 15.6. Prediction confirmed: 15.6 > 10. Step 4: Decide: a "typical" teen in this group sends about 10 texts a day (the median). The mean (15.6) describes the one 60-text day more than the group.

Check yourself — explain it

Why was it possible to predict mean > median before any calculation?

Paired problem — example still visible

Quiz scores: 45, 70, 75, 80, 82, 85, 88, 90, 95. Name the shape, find the mean and median, and choose the typifying value. -> Skewed left (tail at 45). Median = 82 (5th value). Mean = 710 / 9 ≈ 78.9. The median (82) typifies - the mean is pulled down toward the tail.

Faded completion — last step is yours

"Data: 2, 3, 3, 4, 5, 30. Mean = 47 / 6 ≈ 7.8 and median = 3.5. The shape is skewed ___ and the better typical value is ___." -> right; the median (3.5)

Ready to practise?

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

Start practice →Take the unit quiz