1.
3 Grouping data
1 Here are the Maths test results for a group of students.
35, 39, 43, 61, 55, 68, 48, 57, 46, 38, 41, 50, 47, 37, 46
a Copy and complete the Tally and Frequency columns in the grouped tally chart,
using the Maths test results.
Maths result Tally Frequency
30–39
40–49
50–59
60–69
b What is the modal class? ......................
c How many students had test results of 60 or over? ......................
2 Arif asked his classmates how many pets they have.
Here are his results.
a Copy and complete the frequency table,
using data from the graph.
Number of pets Frequency
0–2
3–5
6–8
9–11
b What is the modal class? ......................
c How many classmates had six or more pets? ......................
d Can you tell from Arif’s frequency table how many classmates had five pets?
If so, how?
...................................................................................................................................................
...................................................................................................................................................
© Pearson Education Ltd 2019. Copying permitted for purchasing institution only. This material is not copyright free.
3 Amy carried out a survey of the number of texts that people in her class sent that week.
Here are her results.
Number of
Frequency
texts
0–4 2
5–9 8
10–14 1
15–19 3
20–24 11
25–29 7
a What is the modal class? ......................
b Complete the bar chart for the data.
Give your chart a title.
4 The frequency table shows the weights of students in a Year 7 class, measured to the nearest
kilogram (kg).
Weight (kg) Frequency
20–29 3
30–39 18
40–49 7
50–59 2
a Draw a bar chart for the data.
b What is the modal class? .......................
c Can you tell the weight of the lightest student? If so, how?
...................................................................................................................................................
...................................................................................................................................................
© Pearson Education Ltd 2019. Copying permitted for purchasing institution only. This material is not copyright free.
1.3 Grouping data
1 Arif collects data about the heights of
students in his class.
He used spreadsheet software to draw a bar
chart of his results.
What problems are there with this bar chart?
............................................................................
............................................................................
2 The frequency table shows the heights of some plants.
Height (cm) Frequency
10–14 7
15–19 18
20–24 22
25–29 3
a What is the modal class? ......................
b Toby finds the median height of the plants and says that it is 19 cm.
Can Toby be correct? Explain why.
...................................................................................................................................................
3 Sameer records how many pens students have in their pencil case.
5, 5, 2, 7, 3, 1, 5, 3, 3, 1, 1, 2, 7, 5, 3, 2, 5, 9, 2, 4
a What is the mode? .......................
b Complete the grouped frequency table for the data.
Number of pens Frequency
1-2
3-4
5-6
7-8
9-10
c What is the modal class? .......................
d Is the mode or the modal class a better representation of the data? Explain why.
...................................................................................................................................................
© Pearson Education Ltd 2019. Copying permitted for purchasing institution only. This material is not copyright free.
4 The students in Class 7A went pond dipping.
They counted the tadpoles they caught.
This grouped frequency table shows their results.
Number of
Frequency
tadpoles
0–19 9
20–39 6
40–59 12
60–79 2
80–99 1
a What is the modal class? .......................
The students then decided to group their data into smaller groups
and started to make this frequency table.
Number of
Frequency
tadpoles
0–9
10–19
...
80–89
90–99
Hannah says, ‘The modal class will now be either 40–49 or 50–59.’
b Is Hannah correct? Explain why.
...................................................................................................................................................
© Pearson Education Ltd 2019. Copying permitted for purchasing institution only. This material is not copyright free.
1.3 Grouping data
1 a Complete the table for this set of data.
5, 9, 3, 5, 1, 11, 6, 10, 4, 7, 5, 8, 12, 9, 4
Maths result Tally Frequency
1–3
4–6
7–9
10–12
b Which is the modal class? ......................
2 The grouped bar chart shows the number of spellings
that students got correct in a test.
a What marks are included in the 5–9 group? ......................
b How many students spelt between 10 and 14 words correctly? ......................
c Which group has the most students? ......................
3 Beth investigated the number of phone calls that students made that week.
She recorded her results in a grouped frequency table.
Number of
Frequency
phone calls
0–4 3
5–9 2
10–14 4
15–19 5
20–24 11
25–29 5
a Which group has the highest frequency? .......................
© Pearson Education Ltd 2019. Copying permitted for purchasing institution only. This material is not copyright free.
b Complete the bar chart for the data.
4 The bar chart shows the weights of some apples, in grams.
a How many apples are in the 50–59 group? ......................
b How many apples are in the 70–79 group? ......................
c How many apples are there altogether? ......................
© Pearson Education Ltd 2019. Copying permitted for purchasing institution only. This material is not copyright free.
1.3 Grouping data
Core
1 a
Maths result Tally Frequency
30–39 4
40–49 6
50–59 3
60–69 2
b 40–49 c 2
2 a
Number of pets Frequency
0–2 19
3–5 8
6–-8 2
9–11 1
b 0–2 c 3 d No, we only know they have 3–5 pets.
3 a 20–24 b
4 a
b 30–39 c No, we only know that they weigh somewhere between 20 and 29 kg.
© Pearson Education Ltd 2019. Copying permitted for purchasing institution only. This material is not copyright free.
Depth
1 There should be no gaps between the bars.
2 a 20–24
b Yes. The median will be half way between the 25th and 26th values (when ordered).
The 25th value is between 15 and 19 and the 26th is between 20 and 24, so if the two values were
18 and 20, then the median would be 19.
3 a 5
b
Number of pens Frequency
1–2 7
3–4 5
5–6 5
7–8 2
9–10 1
c 1–2
d The mode is a better representation because the modal class does not contain the mode.
It is also a little lower than the mode.
4 a 40–59
b Hannah is not necessarily right. The 40–59 class will break into two classes, 40–49 and 50–59.
These will have 12 students between them, so one of the classes will have at least 6 students.
If it breaks equally (6 and 6), then these could both be modal classes. But the modal class need not
be one of them. The 0–19 class could break into 1 student in the 0–9 class and 8 students in the
10–19 class, so it is possible that this class is the modal class instead.
Support
1 a
Maths result Tally Frequency
1–3 2
4–6 6
7–9 4
10–12 3
b 4–6
2 a 5, 6, 7, 8 and 9 b 5 c 5–9
3 a 20–24 b
4 a 7 b 5 c 25
© Pearson Education Ltd 2019. Copying permitted for purchasing institution only. This material is not copyright free.
