ESAT Maths 1 · free worked solution

ESAT Maths 1 quartiles: read cumulative frequency

Quartile solution: locate three-quarters of the frequency and interpolate to estimate 35.

Cumulative frequency and quartilesSpecification M6.2Reviewed 5 August 2026

Answer first

Option C

The correct answer is

$35$

For the upper quartile, find three-quarters of the total frequency before reading between the two known points.

This is original UniGenius practice material from the reviewed Maths 1 bank. It is not an official UAT-UK question, past paper, or recalled question.

The question

Read the setup, then choose the shortest valid route

A cumulative-frequency graph has total frequency $80$ . At value $30$ the cumulative frequency is $54$ , and at value $40$ it is $66$ . Estimate the upper quartile.

A $52.5$
B $43.75$
C $35$ Answer
D $36$
E $38$

Worked solution

The route in 3 steps

The upper quartile is the value at cumulative frequency $3(80)/4=60$ .
Between cumulative frequencies $54$ and $66$ , the target $60$ is halfway.
Interpolate halfway between values $30$ and $40: 30+(6/12)\times10=35$ .

Next action

Calibrate your ESAT score

Use the free converter to see what a raw mark may mean on the ESAT scale, then choose your next timed set.

Try the free ESAT score converter

Publication boundary: one independently reviewed, original practice row is exposed on this page; the paid and mock bank inventories remain unlisted.