Histograms Quiz (Grade 7)

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Score: 0 / 10

Histograms — Notes & Worked Examples Show / Hide

Explanation:

In a histogram for grouped continuous data with unequal class intervals, the vertical axis plots Frequency Density rather than frequency, and the area of each bar represents the frequency. Always add a column for class width and use the formula triangle:

Frequency Density = FrequencyClass Width and Frequency = Frequency Density × Class Width. If an interval is cut part-way through (e.g. estimating how many values exceed 25 in a 20 < t ≤ 40 bar), use the fraction of the bar's width.

Example 1: Calculate the frequency densities for the grouped table below.

Mass (m g)	Freq (f)	Width (w)	FD = f ÷ w
0 < m ≤ 10	15	10	1.5
10 < m ≤ 15	20	5	4.0
15 < m ≤ 35	36	20	1.8

Plot bars with heights 1.5, 4.0, and 1.8.

Example 2: Using the table in Example 1, estimate how many items have mass between 12 g and 25 g.

Solution:

Split 12 g to 25 g across both bars:

• 12 to 15 g: 3 × 4.0 = 12

• 15 to 25 g: 10 × 1.8 = 18

Answer: 12 + 18 = 30 items

One Page Guide (PDF) Histograms Worksheets

Question 1

[1 mark]

In a histogram, the class interval 10 < t ≤ 20 has a frequency of 24.
Calculate the frequency density for this class interval.

Worked Solution & Answer

Frequency density = FrequencyClass width = 2410 = 2.4 B1

Answer: 2.4

Question 2

[1 mark]

In a histogram, the class interval 10 < t ≤ 15 has a frequency of 23.
Calculate the frequency density for this class interval.

Worked Solution & Answer

Frequency density = FrequencyClass width = 235 = 4.5 B1

Answer: 4.5

Question 3 AQA Nov 2018 3H Q18

[3 marks]

Here is some information about the ages of people at a concert.
@@TABULAR₀@@

Draw a histogram to represent the information.

Worked Solution & Answer

Calculate frequency density = FrequencyClass width: M1
• 10 ≤ x < 15: width = 5, FD = 85 = 1.6
• 15 ≤ x < 25: width = 10, FD = 2410 = 2.4 M1
• 25 ≤ x < 40: width = 15, FD = 3015 = 2.0
• 40 ≤ x < 70: width = 30, FD = 3930 = 1.3 A1

Answer: Bars drawn with frequency densities: 1.6, 2.4, 2.0, 1.3

Question Paper (PDF) • Mark Scheme (PDF)

Question 4

[3 marks]

The histogram shows some information about the ages of the 134 members of a sports club.

20% of the members of the sports club who are over 50 years of age are female.
Work out an estimate for the number of female members who are over 50 years of age.

Worked Solution & Answer

Members aged 50 to 60 = 10 × 1.4 = 14 M1
Members aged 60 to 90 = 30 × 0.7 = 21 M1
Total members over 50 = 14 + 21 = 35
Number of females over 50 = 20% of 35 = 0.2 × 35 = 7. A1

Answer: 7

Question Paper (PDF) • Mark Scheme (PDF)

Question 5

[3 marks]

The table gives information about the distances, in miles, that some Year 10 students live from school.

(a) On the grid, draw a histogram for this information. [3 marks]

Worked Solution & Answer

(a)

Frequency densities: 90/1 = 90, 48/0.5 = 96, 22/0.5 = 44, 8/1 = 8, 12/2 = 6 M2 A1

Answer (a): Histogram bars of frequency densities 90, 96, 44, 8 and 6

Question Paper (PDF) • Mark Scheme (PDF)

Question 6 IGCSE Specimen 1H Q19

[4 marks]

150 people took part in a survey.
The histogram shows information about the ages of these people.

Work out how many of these 150 people are aged between 50 years and 55 years.

Worked Solution & Answer

In minor grid units (width × height in small squares): 20–30: 10 × 17 = 170 M1
30–50: 20 × 36 = 720
50–55: 5 × 44 = 220 M1
55–70: 15 × 20 = 300
70–80: 10 × 9 = 90 M1
Total area = 170 + 720 + 220 + 300 + 90 = 1500 small squares
Number of people aged 50–55 = (220 / 1500) × 150 = 22. A1

Answer: 22

Question Paper (PDF) • Mark Scheme (PDF)

Question 7 AQA Jun 2025 2H Q19

[4 marks]

The histogram represents the ages of the 500 members of a gym.
The first bar represents the members aged at least 16 and under 20

Each member pays an annual fee based on their age.
@@TABULAR₀@@
Use the histogram to estimate the **total** annual fees paid by these members.

Answer £

Worked Solution & Answer

Members aged 65 to 80: width = 80 – 65 = 15, frequency density = 2.8 ⇒ 15 × 2.8 = 42 members M2
Members under 65 = 500 – 42 = 458 members M1
Total fees = 458 × £275 + 42 × £129 = £125 950 + £5418 = £131 368. A1

Answer: Answer £ 131 368

Question Paper (PDF) • Mark Scheme (PDF)

Question 8

[4 marks]

The histogram gives information about the number of hours some students used their phones last week.
The histogram is incomplete.

28 students used their phones for between 30 and 40 hours.
24 students used their phones for between 40 and 60 hours.

(a) Use this information to complete the histogram. [2 marks]

(b) No student used their phone for more than 60 hours.
Work out the total number of students. [2 marks]

Worked Solution & Answer

(a)

40–60 fd = 24 ÷ 20 = 1.2 (12 small squares) M1 A1

Answer (a): Bar of height 12 small squares (fd = 1.2) drawn from 40 to 60

(b)

Total = (20 × 1.6) + (10 × 3.6) + 28 + 24 = 32 + 36 + 28 + 24 = 120 M1 A1

Answer (b): 120

Question Paper (PDF) • Mark Scheme (PDF)

Question 9

[5 marks]

The table gives information about the heights of 150 students.

(a) On the grid, draw a histogram for this information. [3 marks]

(b) Work out an estimate for the fraction of the students who have a height between 150 cm and 170 cm. [2 marks]

Worked Solution & Answer

(a)

FD = 15÷10 = 1.5, 30÷5 = 6, 51÷5 = 10.2, 36÷5 = 7.2, 18÷15 = 1.2 M2 A1

Answer (a): Histogram with frequency densities 1.5, 6, 10.2, 7.2, 1.2

(b)

30 + 51 + 36 + (5/15 × 18) = 117 + 6 = 123 M1
⇒ 123/150 = 41/50 A1

Answer (b): 123150 (or 4150 or 0.82)

Question Paper (PDF) • Mark Scheme (PDF)

Question 10

[5 marks]

The table gives information about the amount of time that each of 150 people were in a shop.

(a) On the grid, draw a histogram for this information. [3 marks]

(b) Work out an estimate for the fraction of these 150 people who were in the shop for between 20 minutes and 40 minutes. [2 marks]

Worked Solution & Answer

(a)

Frequency densities: 20÷10=2, 70÷20=3.5, 22÷5=4.4, 30÷15=2, 8÷10=0.8 M2 A1

Answer (a): Histogram bars at frequency densities 2, 3.5, 4.4, 2, 0.8

(b)

½×70 + 22 + ⅓×30 = 35 + 22 + 10 = 67 M1
⇒ 67/150 A1

Answer (b): 67150

Question Paper (PDF) • Mark Scheme (PDF)

Score: 0 / 10 (0 / 33 marks)

Histograms Worksheets Next: Conditional probability →

Grade 7 Quizzes

19 Topics

7A - Surds	7B - Bounds
7C - Proportion (harder)	7D - Algebraic fractions
7E - The quadratic formula	7F - Factorising harder quadratics
7G - Trigonometric & exp. Graphs	7H - Rearranging (harder)
7J - Functions (harder)	7K - Iteration
7L - Area of any triangle	7M - The sine rule
7N - The cosine rule	7P - Congruent triangles
7Q - 3D pythagoras / trig.	7R - Histograms
7S - Conditional probability	7T - Exact trig. values (harder)
7U - Area of a segment