Maths Quest A Year 11 for Queensland
WorkSHEET 10.2
Chapter 10 Describing, exploring and comparing data
WorkSHEET 10.2
1
Describing, exploring and comparing data
Name: ___________________________
1
The following data show the survey results of
the number of children in families.
No of children
1
2
3
4
5
6
Total
Data:
3, 5, 2, 4, 3, 1, 4, 1, 2, 5, 3, 6, 4, 3, 5, 4, 4.
Create a frequency table for this data.
2
Tally
ll
ll
llll
llll
lll
l
Frequency
2
2
4
5
3
1
17
Using the frequency table from question 1 find: (a)
( 2  1)  ( 2  2)  ( 4  3)  (5  4)  (3  5)  (1  6)
(a) the mean number of children per family
17
59

17
 3.47
(b) the median number of children per family
(c) the modal number of children per family
3
Lachlan has calculated his mean mathematics
score to be 67%, based on eight tests. If he
scores 75% on the ninth test, what will his new
mean score be?
(b)
1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6,
Median = 4
(c)
Mode = 4
(67  8)  75 611

9
9
 67.88
Lachlan’s new mean score will be 68%.
Maths Quest A Year 11 for Queensland
4
Chapter 10 Describing, exploring and comparing data
A shoe company surveyed the shoe size
purchased by women over a period of time.
The results were as follows:
WorkSHEET 10.2
2
(a)
8 5 6  58 6  7  9 5 7  6 88 6 9  7 8
17
8, 5, 6, 5, 8, 6, 7, 9, 5, 7, 6, 8, 8, 6, 9, 7, and 8.
5
(a)
Calculate the mean of this data
(b)
Find the modal value.
(c)
Find the median value.
(d)
Which of these values would be of the
most use to the company? Why?
118
17
 6.94

The mean shoe size is 7.
Tom has been earning some extra pocket
money by washing cars.
In each hour block he has managed to wash 4
cars, 5 cars, 3 cars, 4 cars and 4 cars.
The mean number of cars that he has been able
to wash is therefore 4 cars per hour.
(b)
The mode is 8
(c)
5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9,
The median value is 7.
(d)
The mode would probably be of the most
value because this is the shoe size that they
sell the most.
45344 x
5
6
20  x
5
6
20  x  30
x  10
In order to increase his mean to 5 cars per hour, Tom needs to wash 10 cars in his next hour.
how many cars does Tom need to wash in the
No, this is not very likely.
next hour? Is this likely?
6
This grouped frequency table gives the number
of ‘salmon cod’ caught by a fisherman on 25
fishing trips.
Number of
Frequency f
salmon cod
20–24
1
25–29
2
30–34
4
35–39
4
40–44
6
45–49
8
Add a cumulative frequency column to the
table, then use this to determine the median
class.
4
Number of
Frequency f
salmon cod
Cumulative
frequency
20–24
1
1
25–29
2
3
30–34
4
7
35–39
4
11
40–44
6
17
45–49
8
25
25  1
th score
2
 13th score
Median 
Median class is 40  44.
Maths Quest A Year 11 for Queensland
7
Chapter 10 Describing, exploring and comparing data
Use the frequency distribution table in
questions 6 to calculate the mean number of
‘salmon cod’ caught by the fisherman on his 25
fishing trips.
WorkSHEET 10.2
Class Frequency
Number of
salmon cod centre (x )
f
fx
20–24
22
1
22
25–29
27
2
54
30–34
32
4
128
35–39
37
4
148
40–44
42
6
252
45–49
47
8
376
f  25
3
fx  980
fx
f
980

25
 39.2
x
8
From the distribution table in question 6,
determine the modal class.
9
The number of goals scored by a team is shown
below:
5, 4, 4, 7, 5, 9, 12, 14, 16, 16.
modal class = 45 – 49 cod.
2
4, 4, 5, 5, 7, 9, 12, 14, 16, 16
LQ
(a) Find the lower quartile.
10
median
UQ
(b) Find the upper quartile.
(a)
Lower quartile = 5
(c) Find the interquartile range.
(b)
Upper quartile = 14
(c)
Interquartile range = 14  5
=9
Use your calculator to find the standard
deviation of the set of outcomes when a
six-sided die is rolled as shown below.
1, 2, 3, 4, 5, 6
State your answer correct to two decimal
places.
1
Standard deviation = 1.87