Mean, Median, Mode & Range from Lists | OCR

All four measures — mean, median, mode and range — from a list of numbers. The unit opener for OCR GCSE Foundation, Year 10 Unit 7 Lesson 1. Built around the one habit pupils most often skip: sort the list before taking the median.

Lists only — no tables or charts yet — so pupils get the definitions genuinely secure before the rest of the unit reuses them. Every later lesson depends on this one.

What’s included:

• Clear definitions of all four measures, including the points pupils miss: the mean can be a decimal that isn’t in the list, a list can have no mode or more than one, and the range measures spread (always positive), not a typical value
• Worked examples for both an odd-length list (median is the middle value) and an even-length list (median is the average of the two middle values)
• Spot the Mistake — three common misconceptions: taking the median without sorting, subtracting the range the wrong way round, and confusing the mode with the largest value
• Four practice lists of increasing trickiness, including even-length lists that need the mid-pair average and unsorted lists that hide the median
• Going Deeper — a work-backwards problem (find a missing value from the mean) that previews Lesson 2, plus a reasoning question on why a mean needn’t be one of the values
• Exit Ticket — a six-value list whose even-length median catches both core skills (sorting and the mid-pair average) in a single answer

Teacher answer key (3 pages):

• Full worked solutions with the sorted line shown for every list
• A suggested lesson timing guide (~55 min)
• Diagnostic notes linking each wrong answer to its underlying misconception
• A built-in sense-check: every average should land between the smallest and largest value
• A marking summary table for fast, consistent marking

EEF-structured, classroom-tested, OCR-aligned.

smartle. @Smartle-Maths