Robinson TuitionExam boards: Edexcel, AQA and OCR
Plotting at class midpoints, reading and comparing.
Learn it first walks you through the method and a worked example, then two warm-up questions with hints. Nothing is counted until you start the sheet.
Watch out: Plotting at the end of each class (20, 40, 60) instead of at the midpoint (10, 30, 50).
The table shows the times, t seconds, that 25 pupils took to solve a puzzle.
| Time (t seconds) | Frequency |
|---|---|
| 0 < t ≤ 20 | 4 |
| 20 < t ≤ 40 | 10 |
| 40 < t ≤ 60 | 8 |
| 60 < t ≤ 80 | 3 |
Draw a frequency polygon for this information.
Midpoint of each class
| (0 + 20) ÷ 2 | = | 10 |
| (20 + 40) ÷ 2 | = | 30 |
| (40 + 60) ÷ 2 | = | 50 |
| (60 + 80) ÷ 2 | = | 70 |
Plot (midpoint, frequency)
(10, 4)
(30, 10)
(50, 8)
(70, 3)
Join in order with straight lines
Polygon through (10, 4), (30, 10), (50, 8), (70, 3)
The table shows the number of minutes, t, that 40 pupils spent on homework one evening.
| Time (t minutes) | Frequency |
|---|---|
| 0 < t ≤ 20 | 6 |
| 20 < t ≤ 40 | 15 |
| 40 < t ≤ 60 | 12 |
| 60 < t ≤ 80 | 7 |
Write down the midpoint of each class.
(lower end + upper end) ÷ 2
| (0 + 20) ÷ 2 | = | 10 |
| (20 + 40) ÷ 2 | = | 30 |
| (40 + 60) ÷ 2 | = | 50 |
| (60 + 80) ÷ 2 | = | 70 |
10, 30, 50, 70
The table shows the lengths, l cm, of 32 runner beans.
| Length (l cm) | Frequency |
|---|---|
| 10 < l ≤ 15 | 3 |
| 15 < l ≤ 20 | 9 |
| 20 < l ≤ 25 | 12 |
| 25 < l ≤ 30 | 8 |
Jamal is going to draw a frequency polygon for this information.
Write down the coordinates of the four points he should plot.
Midpoints
| (10 + 15) ÷ 2 | = | 12.5 |
| (15 + 20) ÷ 2 | = | 17.5 |
| (20 + 25) ÷ 2 | = | 22.5 |
| (25 + 30) ÷ 2 | = | 27.5 |
(midpoint, frequency)
(12.5, 3), (17.5, 9), (22.5, 12), (27.5, 8)
The table shows the heights, h cm, of 30 sunflowers.
| Height (h cm) | Frequency |
|---|---|
| 100 < h ≤ 120 | 4 |
| 120 < h ≤ 140 | 7 |
| 140 < h ≤ 160 | 11 |
| 160 < h ≤ 180 | 6 |
| 180 < h ≤ 200 | 2 |
On the grid, draw a frequency polygon for this information.
Midpoints
110, 130, 150, 170, 190
Plot (midpoint, frequency)
(110, 4), (130, 7), (150, 11)
(170, 6), (190, 2)
Join in order with straight lines
Polygon drawn through the five points
The frequency polygon shows information about the times, t minutes, that some customers spent in a café.
The classes are 0 < t ≤ 10, 10 < t ≤ 20, 20 < t ≤ 30, 30 < t ≤ 40 and 40 < t ≤ 50.
a) Point above midpoint 25
17
b) Read every point
| 6 + 14 + 17 + 9 + 4 | = | 50 |
50
c) Highest point is at 25
20 < t ≤ 30
The table shows the test marks, m, of 28 pupils.
| Mark (m) | Frequency |
|---|---|
| 0 < m ≤ 10 | 3 |
| 10 < m ≤ 20 | 8 |
| 20 < m ≤ 30 | 12 |
| 30 < m ≤ 40 | 5 |
Kai draws a frequency polygon. He plots the points (10, 3), (20, 8), (30, 12) and (40, 5). He joins them with straight lines, then joins (40, 5) back to (10, 3).
Write down two mistakes Kai has made.
Midpoints should be
5, 15, 25, 35
Kai used the ends of the classes
A frequency polygon is not closed
Not at midpoints, and last point joined back to the first
The table shows the distances, d km, that 40 people travel to work.
| Distance (d km) | Frequency |
|---|---|
| 0 < d ≤ 5 | 4 |
| 5 < d ≤ 10 | 14 |
| 10 < d ≤ 15 | 13 |
| 15 < d ≤ 20 | 6 |
| 20 < d ≤ 25 | 3 |
a) Midpoints
2.5, 7.5, 12.5, 17.5, 22.5
(2.5, 4), (7.5, 14), (12.5, 13), (17.5, 6), (22.5, 3)
Points joined with straight lines
b) Highest frequency is 14
5 < d ≤ 10
c) Median is between the 20th and 21st
| 4 + 14 | = | 18 |
| 18 + 13 | = | 31 |
20th and 21st are in the third class
10 < d ≤ 15
The frequency polygons show the times, t minutes, that 30 pupils in Class A and 30 pupils in Class B spent on homework one night.
The classes are 0 < t ≤ 10, 10 < t ≤ 20, 20 < t ≤ 30, 30 < t ≤ 40 and 40 < t ≤ 50.
a) Class B is the dashed line
| 4 + 1 | = | 5 |
5
b) Compare where the peaks are
Class A modal class: 30 < t ≤ 40
Class B modal class: 10 < t ≤ 20
Class A: its polygon is further to the right
The frequency polygon shows information about the masses, m kg, of some parcels.
The classes are 0 < m ≤ 2, 2 < m ≤ 4, 4 < m ≤ 6 and 6 < m ≤ 8.
a)
| 4 + 9 + 8 + 4 | = | 25 |
25
b) midpoint × frequency
| 1 × 4 | = | 4 |
| 3 × 9 | = | 27 |
| 5 × 8 | = | 40 |
| 7 × 4 | = | 28 |
| total | = | 99 |
| mean | = | 99 ÷ 25 |
| mean | = | 3.96 |
3.96 kg
Some students measured the heights, h cm, of 40 plants.
The classes are 0 < h ≤ 10, 10 < h ≤ 20, 20 < h ≤ 30, 30 < h ≤ 40 and 40 < h ≤ 50.
The frequency polygon on the grid is not finished: the point for the class 40 < h ≤ 50 is missing.
a) Add the frequencies shown
| 5 + 9 + 12 + 8 | = | 34 |
| 40 - 34 | = | 6 |
6
b) Midpoint of 40 < h ≤ 50 is 45
Plot (45, 6)
Join (35, 8) to (45, 6)
The frequency polygon shows the times, t minutes, that 60 runners took to finish a fun run.
The classes are 10 < t ≤ 20, 20 < t ≤ 30, 30 < t ≤ 40 and 40 < t ≤ 50.
Lena says, "More than half of the runners took longer than 30 minutes."
a) Classes above 30 minutes
| 21 + 12 | = | 33 |
33
b)
| half of 60 | = | 30 |
33 > 30
Yes, Lena is correct
Answer the questions above and your score appears here.
Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper. It is not on the Edexcel International GCSE (4MA1).