L2 · Mean or Median? Choosing by Shape

Learning goal

“I can choose the statistic that best typifies a data set - mean, median, or mode - and justify the choice from the distribution's shape: in a symmetric distribution the mean and median are equal; in a skewed distribution the mean is pulled toward the tail, so the median (or the mode, for categories) usually typifies better.”

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

Tail — the stretched-out side of a skewed distribution, where the few far-away values sit.

Outlier — a value that lies far from the rest of the data.

Pulled — what happens to the mean when a tail or outlier drags it away from the pile of data, because the mean is calculated from EVERY value.

Worked example

Ages of 9 chess club members: 11, 12, 12, 13, 13, 13, 14, 14, 15. Step 1: Shape first. Counts by age: 11: one, 12: two, 13: three, 14: two, 15: one - 1, 2, 3, 2, 1 mirrors around 13, so the distribution is symmetric. Step 2: Mean: sum = 11 + 12 + 12 + 13 + 13 + 13 + 14 + 14 + 15 = 117; 117 / 9 = 13. Step 3: Median: the 5th of 9 ordered values = 13. Mode: 13. Step 4: In a symmetric distribution the mean and median are EQUAL - both flags land on 13. Either statistic typifies this data honestly. Say it plainly: symmetry means the balance point (mean) and the middle value (median) are the same point. Choosing between them only becomes a real decision when the shape is skewed.

Check yourself — explain it

Why do the mean and median agree here?

Paired problem — example still visible

Heights of 9 plants (cm): 140, 145, 145, 150, 150, 150, 155, 155, 160. Find the mean and median, and say which statistic(s) typify the heights. -> Mean = 1350 / 9 = 150 cm; median = 150 cm. The distribution is symmetric (counts 1, 2, 3, 2, 1 around 150), so either typifies; the typical height is 150 cm.

Faded completion — last step is yours

"Data: 6, 8, 8, 10, 10, 10, 12, 12, 14. Mean = 90 / 9 = ___; median = ___. The shape is symmetric, so the two statistics ___." -> 10; 10; agree (are equal)

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