Edexcel 4MA1Statistics15 Questions

Histograms — Unequal Classes

Progressive test · Grades 5–9 · Frequency Density Mastery

Score Progress0 / 15 correct

📐 Formula Reference

FD = Frequency ÷ Class Width

Use to find bar height

Frequency = FD × Class Width

Area of bar = Frequency

ANCHOR

Questions 1–5 · Grades 5–6 · Core FD Calculations

⚓

Q1Q1 — Calculate Frequency Density

Grade 5

A class interval has a Frequency of 24 and a Class Width of 4. Calculate the Frequency Density.

Class Width	Frequency	Frequency Density
4	24	?

Q2Q2 — Calculate Frequency Density

Grade 5

The class interval 10 ≤ t < 25 has a frequency of 45. Calculate the Frequency Density.

Class Interval	Class Width	Frequency	Frequency Density
10 ≤ t < 25	15	45	?

Q3Q3 — Calculate Frequency Density

Grade 5

The class interval 30 ≤ w < 50 has a frequency of 100. Calculate the Frequency Density.

Interval	Freq	FD
30 ≤ w < 50	100	?

Q4Q4 — Find Frequency from FD

Grade 5

A histogram bar has a Frequency Density of 3.5 and the class width is 8. Calculate the Frequency.

Class Width	FD	Frequency
8	3.5	?

⚠️ TRAP: Never read bar HEIGHT as Frequency. In histograms, AREA = Frequency.

Q5Q5 — Find Frequency from FD

Grade 5

A bar covers the interval 20 ≤ x < 35 and has a Frequency Density of 4. Calculate the Frequency.

Interval	Class Width	FD	Frequency
20 ≤ x < 35	15	4	?

⚠️ TRAP: Always subtract to find Class Width — do not assume it equals 10.

HIGHER STANDARD

Questions 6–10 · Grades 6–7 · Reading & Completing Histograms

🔀

Q6Q6 — Missing Frequency from Histogram

Grade 6

The table below is incomplete. Using the histogram (bar heights given), find the missing frequency for 40 ≤ t < 60.

Interval	Class Width	FD (bar height)	Frequency
20 ≤ t < 30	10	5	50
30 ≤ t < 40	10	8	80
40 ≤ t < 60	20	3	?
60 ≤ t < 70	10	4	40

⚠️ TRAP: The bar for 40 ≤ t < 60 is WIDER — same height ≠ same frequency!

Q7Q7 — Missing Frequency from Histogram

Grade 6

The histogram shows bars for the weight (kg) of parcels. The bar for 2 ≤ w < 5 has a height (FD) of 6. Find the frequency for this class.

Interval	Class Width	FD	Frequency
0 ≤ w < 2	2	8	16
2 ≤ w < 5	3	6	?
5 ≤ w < 8	3	4	12

Q8Q8 — Missing Frequency (Multi-bar Table)

Grade 7

The table is partially completed. The total number of students surveyed is 200. Use this to find the missing frequency for 50 ≤ m < 80.

Interval	Class Width	FD	Frequency
0 ≤ m < 20	20	2	40
20 ≤ m < 50	30	3	90
50 ≤ m < 80	30	?	?
80 ≤ m < 100	20	1	20

⚠️ TRAP: Use the TOTAL to find the missing frequency first, THEN calculate FD.

Q9Q9 — Find Missing Bar Height (FD)

Grade 6

Complete the histogram. The class 60 ≤ t < 65 has a frequency of 35. What height should the bar be drawn at?

Interval	Class Width	Frequency	FD (bar height)
50 ≤ t < 55	5	20	4
55 ≤ t < 60	5	30	6
60 ≤ t < 65	5	35	?
65 ≤ t < 75	10	40	4

Q10Q10 — Complete the Histogram (Two Missing Bars)

Grade 7

The frequency table below has two missing FD values. Calculate both bar heights for 10 ≤ x < 30 and 50 ≤ x < 70.

Interval	Class Width	Frequency	FD
0 ≤ x < 10	10	15	1.5
10 ≤ x < 30	20	60	?
30 ≤ x < 50	20	80	4
50 ≤ x < 70	20	30	?

GRADE 9 KILLER

Questions 11–15 · Grades 8–9 · Estimation, Ratio & Median

⚡

Q11Q11 — Estimating Proportion (Split Bar)

Grade 8

The class interval 60 ≤ w < 80 has a frequency of 40 (class width = 20, FD = 2). Estimate the number of people with weight between 65 kg and 80 kg. Assume uniform distribution within the class.

Interval	Class Width	FD	Frequency
60 ≤ w < 80	20	2	40

⚠️ TRAP: You CANNOT read 65–80 directly from the histogram — you must SPLIT the bar using proportion.

Q12Q12 — Estimating Proportion (Two Bars)

Grade 8

Using the table below, estimate how many people have a time between 25 and 45 minutes. Assume uniform distribution within each class.

Interval	Class Width	FD	Frequency
20 ≤ t < 30	10	4	40
30 ≤ t < 50	20	3	60

⚠️ TRAP: 25–45 crosses a class boundary — always handle each class SEPARATELY.

Q13Q13 — Ratio Problem (Area of Bars)

Grade 9

Bar A covers 10 ≤ x < 30 with Frequency Density = 5. Bar B covers 30 ≤ x < 40 with unknown frequency. The area of Bar A is twice the area of Bar B. Find the frequency of Bar B.

Bar	Interval	Class Width	FD	Frequency (Area)
A	10 ≤ x < 30	20	5	?
B	30 ≤ x < 40	10	?	?

⚠️ TRAP: 'Area of bar' = Frequency. The ratio of AREAS = ratio of FREQUENCIES.

Q14Q14 — Ratio Problem (Find Missing FD)

Grade 9

The frequency of class 0 ≤ t < 20 is three times the frequency of class 20 ≤ t < 30. The FD of the first class is 4.5. Find the FD of the second class.

Interval	Class Width	FD	Frequency
0 ≤ t < 20	20	4.5	?
20 ≤ t < 30	10	?	?

⚠️ TRAP: Never assume FDs are in the same ratio as frequencies — class widths differ!

Q15Q15 — Median from Histogram

Grade 9

The histogram below shows the distribution of 160 students' exam scores. Estimate the median score.

Interval	Class Width	FD	Frequency
0 ≤ s < 20	20	1	20
20 ≤ s < 40	20	2	40
40 ≤ s < 60	20	3	60
60 ≤ s < 80	20	1.5	30
80 ≤ s < 100	20	0.5	10

⚠️ TRAP: Don't just find the middle CLASS — you must INTERPOLATE within the class.

Final Score

0/15

📚 Keep Practising

0% — Focus on the Anchor questions first.

Sign In to Keep Going

You've reached the end of the free preview. Sign in — and upgrade to Plus or Pro — to keep going with Math4MA1.

Full Access

Unlock all 158 lessons

Get Plus or Pro Access