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Middle Years

13.03 Summarising data

Worksheet
Mean
1

Calculate the mean of the following data sets:

a

6, \, 4

b

8, \, 5

c

4, \, 8, \, 9, \, 12

d

7, \, 18, \, 9, \, 3

e

4, \, 10, \, 2, \, 9, \, 5

f

6, \, 14, \, 10, \, 13, \, 5, \, 9, \, 14, \, 15

g

11, \, 5, \, 14, \, 18, \, 15

h

8, \, 14, \, 24, \, 7, \, 12

i

13, \, 27, \, 9, \, 6, \, 8

j

13, \, 15, \, 7, \, 17, \, 9

2

State the mean of the following sets of data:

a

9, 9, 9, 9

b

2, 3, 4

c

850, 900, 950

3

Martha's grades in her 5 subjects are: 91, 93, 94, 90 and 92. Find the mean of Martha's grades.

4

Victoria has scored 12 goals this season, with a mean of 2 goals per game. How many games did she play?

5

James has played 10 games this season, with a mean of 1.5 goals per game. How many goals did he score in total?

Median
6

Find the median of the following data sets:

a

2, \, 3, \, 4, \, 5, \, 6

b

6, \, 9, \, 3, \, 5, \, 4

c

1, \, 4, \, 6, \, 8

d

5, \, 5, \, 5, \, 5

e

22, \, 12, \, 19, \, 16

f

2, \, 4, \, 9, \, 10

g

3, \, 18, \, 10, \, 19, \, 12, \, 5, \, 6, \, 20, \, 7

h

7, \, 19, \, 6, \, 14, \, 18, \, 11

i

5.3, \, 8.4, \, 2.6, \, 4.7, \, 3.5

j

49.4, \, 25.4, \, 47.2, \, 34.2, \, 28.4, \, 32.2

7

A set of 15 scores is arranged in increasing order. In what position does the median score lie?

8

A set of 23 scores is arranged in increasing order. In what position does the median score lie?

9

A set of 12 scores is arranged in increasing order. Between which two scores does the median score lie?

10

A set of 34 scores is arranged in increasing order. Between which two scores does the median score lie?

11

Counting numbers in increasing order such as 4, 5, 6, 7 are called consecutive numbers. Write down five consecutive numbers whose median is 6.

12

Write down four consecutive odd numbers whose median is 12.

13

Write down four consecutive even numbers whose median is 15.

14

Find the median from the following frequency distribution tables:

a
Score1213141516
Frequency12345
b
Score1516171819
Frequency14144
c
Score1516171819
Frequency27315
d
Score1516171819
Frequency12552
e
Score1415161718
Frequency12551
f
Score1314151617
Frequency54135
Mode and range
15

Calculate the range of the following scores:

10, 16, 6, 18, 17, 11, 9, 15, 14
16

Write down four whole numbers whose median is 14 and whose range is 3.

17

Write down four whole numbers whose median is 17 and whose range is 3.

18

For each of the following data sets, calculate:

i

The median

ii

The mode

iii

The range

a
Score1114192229
Frequency10134712
b
Score1419222532
Frequency91412110
19

A phone support centre tracks the length of calls made each day in minutes. During a shift one employee made calls of the following lengths:

2, \, 3, \, 3, \, 2, \, 2, \, 4, \, 4, \, 2, \, 5, \, 13

a

How many calls did the employee make during their shift?

b

Calculate the following for the length of calls made:

i

Mean

ii

Median

iii

Mode

iv

Range

20

A student scored the following grades on his end of year tests:

87, \, 90, \, 85, \, 84, \, 89, \, 80, \, 85, \, 87, \, 87
a

How many tests did the student take?

b

Calculate the following:

i

Mean

ii

Median

iii

Mode

iv

Range

21

A statistician organised a set of data into a frequency table:

Score3132333435
Frequency121472015
a

Find the total number of respondents the statistician surveyed.

b

Determine the following, rounding your answers to two decimal places:

i

Mean

ii

Median

iii

Mode

iv

Range

22

The television show "Dragon Duels" ran for three seasons, each with 6 episodes. The average fan ratings (out of 10) for each episode are shown in the following table:

Episode 1Episode 2Episode 3Episode 4Episode 5Episode 6
Season 18.28.47.97.988.2
Season 28.28.69.17.88.88.4
Season 38.99.49.29.77.44.3
a

Which season has the highest mean rating?

b

Which season has the highest median rating?

c

Which season has the highest range of ratings?

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