Maths

Statistics (Higher)

Edexcel 1MA1 S

GCSE Maths (1MA1) · Higher · exam-style practice, examiner-report intelligence and the tools that drill it.

Verified against Edexcel 1MA1 (2026 spec)

The topic on one screen

  • Histograms use frequency density =frequencyclass width= \dfrac{\text{frequency}}{\text{class width}} — the yy-axis is never plain 'frequency' on a Higher histogram.
  • Estimated mean from a grouped table: midpoints, then ∑fx∑f\dfrac{\sum fx}{\sum f}. It's an ESTIMATE because the raw values are lost.
  • Cumulative frequency is plotted at the UPPER boundary of each class, never the midpoint.
  • On a CF curve: median at n2\dfrac{n}{2}, lower quartile at n4\dfrac{n}{4}, upper quartile at 3n4\dfrac{3n}{4}, and IQR=UQ−LQ\text{IQR} = \text{UQ} - \text{LQ}.
  • Comparing distributions: compare an average AND a measure of spread, in context — two sentences, not one.
  • Correlation is not causation — write 'as xx increases, yy tends to increase', never 'xx causes yy'.

Where students actually lose marks

Plotting frequency instead of frequency density is the single biggest lost-marks error on Higher histograms — and the reverse when reading a frequency back off a bar.

Edexcel 1MA1 Higher — recurring histogram error

A comparison that gives only an average is capped at half marks: full marks need a second comparison of spread (IQR or range) as well — and each comparison only scores if it is written in context.

Edexcel 1MA1 mark-scheme conventions (comparing distributions)

An estimated mean must be stated as an estimate, and must use class MIDPOINTS — using class boundaries or forgetting the wording both drop marks.

Edexcel 1MA1 Higher — recurring grouped-data error

Try it — exam-style

Medium
3 marks
ORIGINAL

A survey records time tt minutes: 0<t≤100 < t \le 10 (frequency 6), 10<t≤2010 < t \le 20 (14), 20<t≤3020 < t \le 30 (20), 30<t≤4030 < t \le 40 (10). Work out an estimate of the mean time.

Medium
2 marks
ORIGINAL

On a histogram, the bar for the class 15<x≤2515 < x \le 25 has a frequency density of 3.2. How many data values are in this class?

Easy
2 marks
ORIGINAL

A cumulative frequency graph is drawn for 60 students' test scores. The lower quartile is read as 34 marks and the upper quartile as 58 marks. Write down the interquartile range, and state the quartile positions used.

Medium
2 marks
ORIGINAL

Class A test scores have median 62 and IQR 15. Class B have median 55 and IQR 24. Write two comparisons, in context.

Medium
3 marks
ORIGINAL

A scatter graph of revision hours (xx) against test mark (yy) shows positive correlation. A line of best fit passes through (2,30)(2, 30) and (8,66)(8, 66). Estimate the mark for a student who revised for 5 hours, and say whether the estimate is reliable.

Hard
3 marks
ORIGINAL

For the grouped table 0<t≤100 < t \le 10 (frequency 6), 10<t≤2010 < t \le 20 (14), 20<t≤3020 < t \le 30 (20), 30<t≤4030 < t \le 40 (10), estimate the median using linear interpolation.

Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.

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Drill it properly

Mental Maths Trainer

The quick arithmetic estimated means and interpolation rely on.

Rounding Trainer

Reading and rounding values off graphs to the right accuracy.

GCSE maths flashcards

Frequency density, quartile positions and the comparison sentence frame.

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