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Calculate and interpret measures of centre and spread.
Statistics · MA4-DAT-C-02
Sub-topics
Measures of centre
Calculate the mean, median and mode of a data set, and find an unknown value given the mean.
Measures of spread
Find and interpret the range and interquartile range (IQR) as measures of spread for a data set.
Open Math
Data analysis
Statistics · MA4-DAT-C-02
Name:
Date:
Measures of centre
Q1
Straightforward
Find the mean of the data set
3
,
7
,
5
,
9
,
6
3, 7, 5, 9, 6
3
,
7
,
5
,
9
,
6
.
Q2
Straightforward
The test scores of five students are
12
,
8
,
15
,
11
,
4
12, 8, 15, 11, 4
12
,
8
,
15
,
11
,
4
. Find the mean score.
Q3
Straightforward
Find the mean of the values
2
,
6
,
4
,
8
2, 6, 4, 8
2
,
6
,
4
,
8
.
Q4
Straightforward
A student records the number of hours of homework done each day for six days:
9
,
3
,
7
,
5
,
11
,
7
9, 3, 7, 5, 11, 7
9
,
3
,
7
,
5
,
11
,
7
. Find the mean number of hours.
Q5
Moderate
Find the median of the data set
3
,
7
,
5
,
9
,
1
3, 7, 5, 9, 1
3
,
7
,
5
,
9
,
1
.
Q6
Moderate
Find the mode of the data set
4
,
2
,
6
,
2
,
8
,
2
,
5
4, 2, 6, 2, 8, 2, 5
4
,
2
,
6
,
2
,
8
,
2
,
5
.
Q7
Moderate
Find the median of the data set
8
,
12
,
6
,
14
,
10
,
4
8, 12, 6, 14, 10, 4
8
,
12
,
6
,
14
,
10
,
4
.
Q8
Moderate
Find the mode of the data set
5
,
3
,
7
,
3
,
9
,
7
,
3
5, 3, 7, 3, 9, 7, 3
5
,
3
,
7
,
3
,
9
,
7
,
3
.
Q9
Challenging
Five numbers have a mean of
8
8
8
. Four of the numbers are
6
,
9
,
7
,
10
6, 9, 7, 10
6
,
9
,
7
,
10
. Find the fifth number.
Q10
Challenging
The mean of four numbers is
12
12
12
. Three of the numbers are
10
,
15
,
9
10, 15, 9
10
,
15
,
9
. Find the fourth number.
Q11
Challenging
Six numbers have a mean of
7
7
7
. Five of them are
4
,
9
,
8
,
5
,
6
4, 9, 8, 5, 6
4
,
9
,
8
,
5
,
6
. Find the sixth number.
Q12
Challenging
Five numbers have a mean of
11
11
11
. Four of them are
14
,
8
,
12
,
9
14, 8, 12, 9
14
,
8
,
12
,
9
. Find the fifth number.
Measures of spread
Q13
Straightforward
Find the range of the data set
5
,
12
,
3
,
9
,
7
5, 12, 3, 9, 7
5
,
12
,
3
,
9
,
7
.
Q14
Straightforward
Find the range of the data set
20
,
6
,
14
,
2
,
18
20, 6, 14, 2, 18
20
,
6
,
14
,
2
,
18
.
Q15
Straightforward
Find the range of the data set
−
3
,
4
,
11
,
0
,
6
-3, 4, 11, 0, 6
−
3
,
4
,
11
,
0
,
6
.
Q16
Straightforward
The scores in a quiz are
8
,
15
,
3
,
22
,
11
8, 15, 3, 22, 11
8
,
15
,
3
,
22
,
11
. Find the range of the scores.
Q17
Moderate
Find the interquartile range (IQR) of the data set
2
,
4
,
6
,
8
,
10
,
12
2, 4, 6, 8, 10, 12
2
,
4
,
6
,
8
,
10
,
12
.
Q18
Moderate
Find the interquartile range (IQR) of the data set
1
,
5
,
9
,
13
,
17
,
21
1, 5, 9, 13, 17, 21
1
,
5
,
9
,
13
,
17
,
21
.
Q19
Moderate
Find the interquartile range (IQR) of the data set
3
,
6
,
8
,
14
,
16
,
20
3, 6, 8, 14, 16, 20
3
,
6
,
8
,
14
,
16
,
20
.
Q20
Moderate
Find the interquartile range (IQR) of the data set
10
,
14
,
18
,
24
,
30
,
36
10, 14, 18, 24, 30, 36
10
,
14
,
18
,
24
,
30
,
36
.
Q21
Challenging
Which data set has the greater range?
Set A:
{
8
,
9
,
10
,
11
,
12
}
\{8, 9, 10, 11, 12\}
{
8
,
9
,
10
,
11
,
12
}
Set B:
{
3
,
7
,
10
,
13
,
17
}
\{3, 7, 10, 13, 17\}
{
3
,
7
,
10
,
13
,
17
}
A.
Set A
B.
Set B
C.
Both sets have the same range
D.
Cannot be determined
Q22
Challenging
Which data set is more consistent?
Set A:
{
15
,
17
,
19
,
21
,
23
}
\{15, 17, 19, 21, 23\}
{
15
,
17
,
19
,
21
,
23
}
Set B:
{
5
,
12
,
19
,
26
,
33
}
\{5, 12, 19, 26, 33\}
{
5
,
12
,
19
,
26
,
33
}
A.
Set A
B.
Set B
C.
Both sets are equally consistent
D.
Cannot be determined
Q23
Challenging
Which data set has the greater IQR?
Set A:
{
4
,
6
,
8
,
10
,
12
,
14
}
\{4, 6, 8, 10, 12, 14\}
{
4
,
6
,
8
,
10
,
12
,
14
}
Set B:
{
2
,
5
,
8
,
11
,
14
,
17
}
\{2, 5, 8, 11, 14, 17\}
{
2
,
5
,
8
,
11
,
14
,
17
}
A.
Set A
B.
Set B
C.
Both sets have the same IQR
D.
Cannot be determined
Q24
Challenging
Two data sets are summarised below.
Set A: range
=
12
= 12
=
12
, IQR
=
4
= 4
=
4
Set B: range
=
10
= 10
=
10
, IQR
=
8
= 8
=
8
Which statement best describes the comparison?
A.
Set A has greater spread by both measures
B.
Set B has greater spread by both measures
C.
Set A has greater overall spread, but Set B has greater spread in the middle 50% of values
D.
Set B has greater overall spread, but Set A has greater spread in the middle 50% of values
Worked solutions and answers at openmath.au/year-7/data-analysis