GCSE
Mathematics
Targeting Grade C
Handling Data
Unit 2 Averages
Can you …
If not you need
TOP: Practise finding averages
from a list of data
• Find mean, median and mode from a table
of data
Practice 1: Find averages from a
table
•Find the median and mode from a grouped
table
Practice 2: Find median and
mode from a grouped table
•Find the mean from a grouped table
Practice 3: Find mean from a
grouped table
Try a test
TAIL
TOP:
For the following lists of data, find the mean, mode and median.
Remember:
Mode = Most common or most frequent number
Median = Middle number AFTER they have been put in
order
Mean = add all the numbers together and then divided
by how many numbers in the list.
1)
1)
412, 426, 435, 412, 427, 428, 435
2)
27, 29, 27, 25, 24, 27, 25, 29
3)
4, 6, 4, 8, 9, 2, 4, 6, 7, 8, 6, 5, 5, 4, 6 3)
101, 106, 99, 108, 76, 87, 102, 93
4)
Are you ready for
the answers ?
Lesson
2)
4)
Mean = 425, Mode = 412 & 435,
Median = 427
Mean = 26.625, Mode = 27,
Median = 27
Mean = 5.6, Mode = 4 & 6,
Median = 6
Mean = 96.5, Mode = none,
Median = 100
Practice 1: Find the mean, median and mode from the following tables.
1)
2)
A shop sells tins of beans at half price. Ten people leaving the shop
are asked how many tins they bought. The table shows their results.
Number of tins of beans bought
0
1
2
3
4
Frequency
2
0
3
4
1
Some students took a mental arithmetic test. Their marks are given in
the table below.
Mark
4
5
6
7
8
9
10
Next
Frequency
2
1
2
4
7
10
3
Why not use the
Greek letter  (or
sigma) instead of
the word ‘total’.
3)
Rosie has 10 boxes of drawing pins. She counted the number of
drawing pins in each box. The results are in the table below.
Lesson
Number of
drawing pins
Frequency
29
2
30
5
31
2
32
1
Practice 2: For the following grouped tables, find the median and modal
classes (modal means mode!)
1)
2)
Lesson
Mark in Test
Frequency
1 – 20
3
21 – 40
10
41 – 60
17
61 – 80
6
81 – 100
4
Total (Σ)
30
Remember:
Finding the cumulative
frequency may help
you find the median
and mode
Temperature °C
Frequency
0–5
22
6 – 10
61
11 – 15
84
16 – 20
74
21 – 25
56
26 – 30
15
Total (Σ)
312
Practice 3: For the following grouped tables, find the mean.
1)
Find the mid-point of the score column first,
then multiply it by the frequency column.
DARTS RESULTS
Score
Frequency
1 – 20
21 – 40
41 – 60
61 – 80
81 – 100
101 – 120
TOTAL
3
17
25
56
8
3
Mid-point X
fX
Next
2)
Mass (kg)
Frequency
60 – 64
4
65 – 69
27
70 – 74
42
75 – 79
60
80 – 84
35
85 – 89
12
Σ
Lesson
Mid-point X
f×X
TAIL
1) For the given tables, work out the mean, median and mode.
Number of pets
Frequency
1–2
5
3–4
8
5–6
12
7–8
14
9 – 10
13
11 – 12
6
13 – 14
2
Σ
Are you ready for
the answers ?
Answers for Q1
Number of pets
Frequency
Mid – point
f×x
1–2
5
1.5
7.5
3–4
8
3.5
28
5–6
12
5.5
66
7–8
14
7.5
105
9 – 10
13
9.5
123.5
11 – 12
6
11.5
69
13 – 14
2
13.5
27
Σ
60
426
Mean = 426 ÷ 60 = 7.1
Median class = 7 – 8
Modal class = 7 – 8
Next
2)
Number of
matches per box
Frequency
47
4
48
20
49
35
50
24
51
17
Σ
100
Are you ready for
the answers ?
Answers for Q2
Number of
matches per box
Frequency
f×x
47
4
188
48
20
960
49
35
1715
50
24
1200
51
17
867
Σ
100
4930
Mean = 4930 ÷ 100 = 49.3
Median = 49
Mode = 49
Lesson