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10.01 Summarising data

Worksheet
Types of data
1

Classify the kind of data these surveys will collect as one of the following:

  • Categorical
  • Discrete numerical
  • Continuous numerical
a

A class was surveyed about what kinds of pet they own.

b

A class was surveyed about how many apps they have on their phone.

c

A class was surveyed about how long they spent on homework last night.

2

Determine whether the following classify as numerical or non-numerical data:

a

Favourite flavours

b

Maximum temperature

c

Daily temperature

d

Types of horses

e

Amount owing on layby

f

Types of vegetables

g

Brands of tablets

h

Types of folders

i

Daily UV index

j

Maximum rainfall

k

Favorite colours

l

Colours of folders

m

Brands of phones

3

Determine whether the following classify as categorical or non-categorical data:

a

Maximum snowfall

b

Daily UV index

c

Types of dogs

d

Favorite colours

e

Amount owing on a purchase

f

Brands of phones

g

Types of fruits

h

Colours of folders

4

For each of these numerical data types, identify whether they are discrete or continuous:

a

Number of classrooms at a school

b

Daily humidity

c

The ages of a group of people in years

d

The time taken to run 200 metres

e

Lengths of cats' whiskers

f

The distance from Earth to Mars

g

How long it takes to fall asleep

h

Amount paid for walking the dog

i

The number of people taller than you

j

The top speed of different motorcycles

k

The size a coin collection

l

The amount of soda you drink in a day

m

The best time for solving a Rubik's cube

n

The hourly pay rate for a particular job

o

Number of views of a YouTube channel

p

The snowfall in your city

q

Number of children in your sports team

r

The strength of an earthquake

s

Amount of money owing on a mortgage

t

Your marks in a Physics test

Mean
5

Find the mean of the following scores:

a

9, 5, 2, 3, 1

b

3, 2, 5, 1, 4

c

4, 5, 6, 7, 3

d

4, 8, 2, 5, 1

6

Find the mean of the following scores:

a

1, 3, 7, 5, 2

b

7, 4, 3, 4, 8

c

9.5, 7.1, 8.8, 2.5, 1.7

d

- 2 , - 8 , - 9 , - 4 , - 7

e

- 9 , 0, 9, - 6 , 6

f

6.2, 6.1, 6.1, 6.9, 6.7

g

0.1,-0.1,0.2,0.3,-0.5

h

-10.5, -5.4, -6.8, -5.2, -3.2

i

56, 89, 95, 71, 75, 84, 65, 83

j

-14, 0, -2, -18, -8, 0, -15, -1

7

The following five numbers have a mean of 11:

11, 13, 9, 13, 9

If a new number is added that is smaller than 9, will the mean will be higher or lower?

8

The following six numbers have a mean of 107:

102, 103, 111, 107, 108, 111

If a new number is added that is larger than 111, will the mean will be higher or lower?

9

The mean of a set of scores is 35 and the sum of the scores is 560. Calculate the number of scores.

10

There are five numbers with a mean of 7. If four of the numbers are 10, 10, 8, 7, find the fifth number.

11

The five numbers 16, 16, 17, 24 \text{ and } 17 have a mean of 18. If a new number is added that is bigger than 24, state whether the mean will become higher or lower.

12

The mean of a set of 41 scores is 18.6. If a score of 71.8 is added to the set, find the new mean. Round your answer to two decimal places.

Median
13

For the following sets of scores:

i

Sort the scores in ascending order.

ii

Find the median.

a

17, 8, 6, 11, 9, 18

b

69.4,66.7,46.6,76.6,52.8,80.6, 63.9

c

44.9,45.6, - 54.8,74.7, - 77.6, -42.6,67.9,40.6

14

Find the median of the following scores:

a

9, 7, 6, 8, 2

b

4, 13, 10, 19, 18, 5

c

3.2, 2.3, 5.5, 4.6, 8.5

d

47.4, 22.2, 39.2, 46.2, 38.4, 35.4

e

- 4 , - 17 , - 11 , 14, 20, 6

f

-1.5, -2.5, -3, -2, -5, -6

15

In a set of 152 scores, between which two scores does the median lie?

16

A set of 69 scores is arranged in ascending order. In what position does the median score lie?

17

Write down 4 consecutive odd numbers whose median is 40.

Mode
18

Find the mode of the following scores:

a

6, 1, 8, 1, 6, 9, 7, 6, 8

b

1.4, 4.2, 7.4, 7.4, 3.5, 1.4, 7.4, 3.5, 3.4

c

- 7 , - 6 , - 2 , - 9 , - 2 , - 8 , - 7 , - 9 , - 9

d

-0.5, -0.2, -0.3, -1.2, -0.5, -0.7, -0.7, -0.5

e

102, 100, 103, 102, 104, 103, 100, 103

f

- 12 , - 12 , - 6 , - 9 , - 7 , - 8 , - 7 , - 9 , - 7

19

Find both modes of the following set of scores:2, \, 2, \, 6, \, 8, \, 8, \, 8, \, 8, \, 12, \, 14, \, 14, \, 14, \, 14, \, 18, \, 18

20

Explain why the following data set does not have a mode:

4, \, 8, \, 1, \, 2, \, 5, \, 9, \, 3, \, 6
Range
21

Find the range of the following scores:

a

7, 12, 9, 19, 11, 4, 8, 15, 3

b

11.9, 15.6, 3.7, 19.6, 18.3, 4.7, 9.1, 12.5, 5.4

c

- 16 , - 3 , - 12 , - 8 , - 11 , - 15 , - 18 , - 5 , - 17

d

11, - 19 , 14, 17, - 11 , 15, 13, - 5 , - 20

22

Find the range of the following scores:

a

10, 7, 2, 14, 13, 15, 11, 4

b

15, - 2 , - 8 , 8, 15, 6, - 16 , 15

c

- 0.5537 , 1.7444, - 0.3381 , 0.7200, - 0.3381 , 1.0435

23

A group of students had a range in marks of 17 and the lowest score was 9. Find the highest score in the group.

24

The range of a set of scores is 8, and the highest score is 19. Find the lowest score in the set.

Applications
25

A rating system of 1 - 3 was used in a survey to determine the usefulness of a new feature. The ten scores shown below are known to have a mode of 1.

3, 2, 3, 2, 1, 3, 1, 1, 2, x

Find the missing score, x.

26

A real estate agent wanted to determine a typical house price in a certain area. He gathered the selling price of some houses (in dollars):

317\,000, \text{ }\text{ }320\,000,\text{ }\text{ } 347\,000,\text{ }\text{ } 360\,000,\text{ }\text{ } 378\,000,\text{ }\text{ } 395\,000,\text{ }\text{ } 438\,000,\text{ }\text{ } 461\,000,\text{ }\text{ } 479\,000,\text{ }\text{ } 499\,000

a

Calculate the mean house price.

b

Determine the median house price.

27

Oprah has been growing watermelons. The weights of the watermelons (in kilograms) are: 15,\text{ }\text{ } 6,\text{ }\text{ } 5,\text{ }\text{ } 2,\text{ }\text{ } 4,\text{ }\text{ } 4,\text{ }\text{ } 5

a

Calculate the median weight of the watermelons.

b

Calculate the mean weight. Round your answer to two decimal places.

28

Durations of calls (in minutes) made in a household were recorded as follows:

5,\text{ }\text{ } 11,\text{ }\text{ } 3,\text{ }\text{ } 9,\text{ }\text{ } 5,\text{ }\text{ } 14,\text{ }\text{ } 5,\text{ }\text{ } 14,\text{ }\text{ } 14,\text{ }\text{ } 3,\text{ }\text{ } 7,\text{ }\text{ } 7,\text{ }\text{ } 7,\text{ }\text{ } 5,\text{ }\text{ } 3,\text{ }\text{ } 3,\text{ }\text{ } 7,\text{ }\text{ } 14,\text{ }\text{ } 5

a

What was the total number of calls made?

b

What was the longest duration of a call?

c

What was the shortest duration of a call?

d

What was the mean duration of a call? Round your answer to two decimal places.

e

What was the modal duration?

f

What was the median duration?

29

Marge grows two different types of bean plants. She records the number of beans that she picks from each plant for 10 days. Her records are as follows:

  • Plant A: 10, \text{ } 4,\text{ } 4, \text{ }5, \text{ }7, \text{ }10,\text{ } 3,\text{ } 3,\text{ } 9,\text{ } 10

  • Plant B: 8,\text{ } 7,\text{ } 5,\text{ } 5,\text{ } 9,\text{ } 7,\text{ } 8,\text{ } 7,\text{ } 5,\text{ } 6

a

What is the mean number of beans picked per day for Plant A? Round your answer to one decimal place.

b

What is the mean number of beans picked per day for Plant B? Round your answer to one decimal place.

c

What is the range for Plant A?

d

What is the range for Plant B?

e

Which plant produces more beans on average?

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Outcomes

VCMSP297

Distinguish between a population and a sample and investigate techniques for collecting data, including census, sampling and observation

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