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Frequency polygons Quiz

Grade 2 • 2P • 10 Questions (23 Marks)

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Score: 0 / 10
Frequency polygons — Notes & Worked Examples Show / Hide

Explanation:

To draw a frequency polygon from a grouped frequency table, first find the midpoint of each class interval by averaging its endpoints: Midpoint = (lower + upper) ÷ 2. Plot each point at (midpoint, frequency).

Join adjacent points in order from left to right using a ruler and straight lines (never a smooth curve). Do NOT join the last point back to the first point, and do not join the ends down to (0, 0).

Example 1: Plot a frequency polygon for this table.

Time (t)fMidPlot
0 < t ≤ 1045(5,4)
10 < t ≤ 20915(15,9)
20 < t ≤ 30625(25,6)
0 4 8 Freq 0 10 20 30 40 Time (t mins)
Plot midpoints (5, 4), (15, 9), (25, 6) and join with straight lines.

Example 2: This frequency polygon for 0–10, 10–20, 20–30, 30–40 has vertices (5, 3), (15, 8), (25, 11), (35, 6). Find total frequency & modal class.

0 4 8 12 Freq 0 10 20 30 40 (25, 11)
• Total: 3 + 8 + 11 + 6 = 28;  Modal class: 20 < t ≤ 30 (peak 11)
Question 1
[2 marks]
The table shows information about the distances that 60 people travel to work.
@@TABULAR0@@
01020304050102030Distance (d miles)Frequency
Draw a frequency polygon for the information in the table.
Worked Solution & Answer
Plot frequency at each interval midpoint: (5, 12), (15, 25), (25, 10), (35, 8), (45, 5) and connect with straight line segments. M1 A1
01020304050102030Distance (d miles)Frequency
Answer: Points plotted at (5, 12), (15, 25), (25, 10), (35, 8), (45, 5) and joined with line segments
Question Paper (PDF) • Mark Scheme (PDF)
Question 2
[2 marks]
The table shows information about the times, in minutes, 100 people took to complete a
bike race.
Time (t minutes)Frequency120 ⩽ t < 14012140 ⩽ t < 16028160 ⩽ t < 18030180 ⩽ t < 20022200 ⩽ t < 2208
1201401601802002200102030FrequencyTime (t minutes)
On the grid below, draw a frequency polygon for this information.
Worked Solution & Answer
Plot midpoints (130, 150, 170, 190, 210) against frequencies M1 A1
Answer: Points plotted at (130, 12), (150, 28), (170, 30), (190, 22), (210, 8) and joined with straight lines
Question Paper (PDF) • Mark Scheme (PDF)
Question 3
[2 marks]
The table gives information about the speeds of 70 cars.
Speed (s mph)Frequency0 < s ⩽ 101410 < s ⩽ 201820 < s ⩽ 302630 < s ⩽ 4012
010203040102030Speed (mph)Frequency
Draw a frequency polygon for this information.
Worked Solution & Answer
Plot midpoints (5, 14), (15, 18), (25, 26), (35, 12) and join with straight lines. M1 A1
Answer: Points (5, 14), (15, 18), (25, 26), (35, 12) plotted at midpoints and joined with straight line segments
Question Paper (PDF) • Mark Scheme (PDF)
Question 4
[2 marks]
The table shows some information about the weights of 50 potatoes.
Weight (w grams)Frequency10 < w ⩽ 20620 < w ⩽ 302130 < w ⩽ 401340 < w ⩽ 50750 < w ⩽ 603Iveta drew this frequency polygon for the information in the table.The frequency polygon is not fully correct.1020304050600102030Weight (w grams)
Write down **two** things that are wrong with the frequency polygon.
Worked Solution & Answer
Check midpoints and frequencies: (15, 6) was plotted at (15, 8) M1
first and last points are joined by a baseline
vertical axis is unlabelled. C1
Weight (w grams)Frequency10 < w ⩽ 20620 < w ⩽ 302130 < w ⩽ 401340 < w ⩽ 50750 < w ⩽ 603Iveta drew this frequency polygon for the information in the table.The frequency polygon is not fully correct.1020304050600102030Weight (w grams)
Answer: 1. The first point is plotted at (15, 8) instead of (15, 6). 2. The polygon should not be closed (there should not be a line joining the first and last points) / the vertical axis has no 'Frequency' label.
Question Paper (PDF) • Mark Scheme (PDF)
Question 5
[2 marks]
The table shows information about the daily rainfall in a town for 60 days.
Rainfall (R mm)Frequency0 ⩽ R < 585 ⩽ R < 102410 ⩽ R < 151315 ⩽ R < 201120 ⩽ R < 254
0510152025102030Rainfall (R mm)Frequency
Draw a frequency polygon for this information.
Worked Solution & Answer
Midpoints: 2.5, 7.5, 12.5, 17.5, 22.5 M1 A1
Answer: Points plotted at (2.5, 8), (7.5, 24), (12.5, 13), (17.5, 11), (22.5, 4) and joined with straight line segments
Question Paper (PDF) • Mark Scheme (PDF)
Question 6
[2 marks]
The table gives information about the lengths, in cm, of some pieces of string.
Length (t cm)Frequency0 < t ⩽ 101510 < t ⩽ 202020 < t ⩽ 305030 < t ⩽ 402540 < t ⩽ 505Amos draws a frequency polygon for the information in the table.Lengths of pieces of string010203040501020305060FrequencyLength (cm)
Write down **two** mistakes that Amos has made.
Worked Solution & Answer
Vertical axis jumps from 30 to 50 (missing 40) M1
last class 40 < t ⩽ 50 has midpoint 45, not 50 C1
Length (t cm)Frequency0 < t ⩽ 101510 < t ⩽ 202020 < t ⩽ 305030 < t ⩽ 402540 < t ⩽ 505Amos draws a frequency polygon for the information in the table.Lengths of pieces of string010203040501020305060FrequencyLength (cm)
Answer: 1. 40 is missing on the vertical (frequency) axis. 2. The last point is plotted at (50, 5) instead of the midpoint (45, 5).
Question Paper (PDF) • Mark Scheme (PDF)
Question 7 Practice Set 5 3H Q2
[2 marks]
Helen went on 35 flights in a hot air balloon last year.
The table gives some information about the length of time, t minutes, of each flight.
Length of time (t minutes)Frequency0 < t ≤ 10610 < t ≤ 20920 < t ≤ 30830 < t ≤ 40740 < t ≤ 50501020304050246810Time (t minutes)Frequency
On the grid below, draw a frequency polygon for this information.
Worked Solution & Answer
Midpoints: 5, 15, 25, 35, 45 plotted against frequencies 6, 9, 8, 7, 5 M1 A1
01020304050246810Time (t minutes)Frequency
Answer: Points plotted at (5, 6), (15, 9), (25, 8), (35, 7), (45, 5) and joined with straight line segments
Question Paper (PDF) • Mark Scheme (PDF)
Question 8 Specimen Set 1 2F Q23 / 2H Q4
[3 marks]
The grouped frequency table gives information about the heights of 30 students.
Height (h cm)Frequency130 < h ⩽ 1401140 < h ⩽ 1507150 < h ⩽ 1608160 < h ⩽ 17010170 < h ⩽ 1804
(a) Write down the modal class interval. [1 mark]
(b) Write down two things wrong with this incorrect frequency polygon. [2 marks]
120130140150160170180190024681012Height (h cm)Frequency
Worked Solution & Answer
(a)
Highest frequency is 10 in 160 < h ≤ 170 B1
Answer (a): 160 < h ≤ 170
(b)
Midpoints are 135, 145, 155, 165, 175. M1 C1
Answer (b): 1. Points have been plotted at the lower bounds instead of midpoints. 2. The polygon should not be closed (line joining first and last points).
Question Paper (PDF) • Mark Scheme (PDF)
Question 9
[3 marks]
The table shows information about the heights of 80 children.
Height (h cm)Frequency130 < h ⩽ 1404140 < h ⩽ 15011150 < h ⩽ 16024160 < h ⩽ 17022170 < h ⩽ 18019
(a) Find the class interval that contains the median. [1 mark]
(b) Draw a frequency polygon for the information in the table. [2 marks]
1301401501601701800102030Height (h cm)Frequency
Worked Solution & Answer
(a)
40th/40.5th value lies in 160 < h ⩽ 170 (cumulative frequencies: 4, 15, 39, 61, 80) B1
Answer (a): 160 < h ⩽ 170
(b)
Plot midpoints (135, 4), (145, 11), (155, 24), (165, 22), (175, 19) and join with straight lines M1 A1
1301401501601701800102030Height (h cm)Frequency
Answer (b): Points (135, 4), (145, 11), (155, 24), (165, 22), (175, 19) plotted and joined with straight line segments
Question Paper (PDF) • Mark Scheme (PDF)
Question 10
[3 marks]
The table shows information about the heights of 80 plants.
Height (h cm)Frequency10 < h ≤ 20720 < h ≤ 301330 < h ≤ 401440 < h ≤ 501250 < h ≤ 601660 < h ≤ 7018
(a) Find the class interval that contains the median. [1 mark]
(b) On the grid, draw a frequency polygon for the information in the table. [2 marks]
0102030405060705101520FrequencyHeight (h cm)
Worked Solution & Answer
(a)
Cumulative frequencies: 7, 20, 34, 46 ⇒ 40th/41st values lie in 40 < h ≤ 50 B1
Answer (a): 40 < h ≤ 50
(b)
Points (15, 7), (25, 13), (35, 14), (45, 12), (55, 16), (65, 18) plotted at midpoints and joined with straight line segments M1 A1
0102030405060705101520FrequencyHeight (h cm)
Answer (b): Points (15, 7), (25, 13), (35, 14), (45, 12), (55, 16), (65, 18) plotted at midpoints and joined with straight line segments
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 23 marks)
Frequency polygons Worksheets Next: Unitary method →

Grade 2 Quizzes

19 Topics
2A - Calculation problems2B - Using a calculator
2C - Systematic listing2D - Fraction of an amount
2E - FDP2F - Simplifying algebra
2G - Writing an expression2H - Function machines
2J - Solving one step equations2K - Angles
2L - Area and perimeter2M - Reading scales
2N - Probability & Probability Scale2P - Frequency polygons
2Q - Unitary method2R - Bar charts
2S - Pie charts2T - Averages
2U - Stem and leaf diagrams