worksheet 12.1 representing and interpreting …worksheet 12.1 representing and interpreting data...

© John Wiley & Sons Australia, Ltd 1

WorkSHEET 12.1 Representing and interpreting data

Name: ___________________________ Fluency 1 In each of the following, state if the

information was obtained by census or survey. a A school council conducts an election

for a new president. Every council member casts a vote.

b 200 people entering a car park complete a questionnaire on the place they shop most frequently.

c A match box producer tests every fiftieth match box to see if the correct number of matches has been included.

d The manager of a book shop records the number of sales in one day.

Answers: a Census b Survey c Survey d Census

2 In each of the following, state if the information was obtained by census or survey. a A light globe manufacturer tests every

thousandth globe to see if it is faulty. b The number of computer sales is

recorded for a month by the accountant of a computer store.

c A tennis club conducts an election for a new secretary. Every member casts a vote.

d 25 people entering a cinema complete a questionnaire on the type of mobile phone they use.

Answers: a Survey b Census c Census d Survey

3 A survey is to be done about the food at the school canteen. Choose the most appropriate survey method: A survey given to students as they buy something from the canteen. A survey done by PC teachers, with all students, in all classes. Justify your selection.

Answer: A survey done by PC Teachers, with all

students, in all classes. Just surveying people who buy the canteen food is BIASED, because if they are buying food, they must like the food. This survey ignores students who do not buy canteen food, who may not like the food. A survey needs to obtain information from a random sample of ALL students.



4 The school would like feedback about the school’s formal uniform policy. Would it be appropriate for the school to ask just Mrs Hodgson to survey her Year 12 Outdoor Ed students about the Formal Uniform policy?

Explain your answer.

NO! The outdoor Ed students don’t wear the Formal Uniform anyway, so this would be a Biased survey. The survey needs to ask a random sample from ALL students across the whole school.

5 The Mode is the most common Number. It’s easy to find. There is NO rule, it’s just the Most Common number and you just need to look for it! You don’t even need to know what the data is about! What is the mode here?

The mode is the most common number - 180

6 The Mode for the following is:

x Frequency 6 12 8 4 10 3 12 2

The Mode is the most common. Here the most common piece of data is the number 6. There are twelve number 6’s in this data. The data from the table looks like: 6 6 6 6 6 6 6 6 6 6 6 6 8 8 8 8 10 10 10 12 12 Can you see there are more 6’s than any other number?



7 You can find the Mode from a Frequency Distribution Table (FDT), more commonly known as a tally chart. What is the Mode here?

The mode is the most common. Here the number 7 appears six times in the data. Mode = 7

8 You can even have two modes. This is known as bi-modal data. What is the mode here?

Here, both the number 2 and the number 7 appears 3 times in the data. So the Mode is 2 and 6.

9 Data representing the number of pets that a year 8 class has is shown below: 0, 1, 3, 2, 1, 0, 1, 2, 0, 1, 2, 0 If the class gets a new student with 14 pets, without doing any calculations, would the mean: A: increase, B: decrease or C: remain unchanged.

A: increase. Here, the student with 14 pets is an Outlier and you should be able to “see” that the mean would increase. You are allowed to say that the big outlier would increase the mean without actually doing any maths! So you can simply say that: “A big outlier increases the mean”



10 Data representing the number of texts our year 8 class receives on their phone for the day could look like; 20, 14, 33, 42, 31, 29, 40, 28, 37 If we include Mr Finney’s texts of 2, without doing any calculations, would the mean: A: increase, B: decrease or C: remain unchanged.

B: decrease. Here, Mr Finney’s 2 texts is an Outlier and you should be able to “see” that the mean would decrease. You are allowed to say that the Smaller outlier would decrease the mean without actually doing any maths! So you can simply say that: “A small outlier decreases the mean”

11 Data representing the number of texts our year 8 class receives on their phone for the day could look like; 20, 14, 33, 42, 31, 29, 40, 28, 37 If we include Mr Finney’s texts of 2, would the median: A: increase, B: decrease or C: remain unchanged.

*** CARE *** You can’t see what happens to the Median. You have to work it out! 1st, put the data into order; 14, 20, 28, 29, 31, 33, 37, 40, 42 Our Median starts as the number … 31. Now re-do the median with the new piece of data; 2, 14, 20, 28, 29, 31, 33, 37, 40, 42 Now our Median is the number … 30. So, in this instance, the lower outlier reduces the median J You need to show your calculations for calculating both medians!



12 Data representing the number of pets that a year 8 class has is shown below: 0, 1, 3, 2, 1, 0, 1, 2, 0, 1, 2, 0 If the class gets a new student with 14 pets, would the median: A: increase, B: decrease or C: remain unchanged.

*** CARE *** You can’t see what happens to the Median. You have to work it out! 1st, put the data into order; 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3 Our Median starts as the number … 1. Now re-do the median with the new piece of data; 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 14 Now our Median is the number … 1. So, in this instance, the higher outlier does NOTHING to the median J You need to show your calculations for calculating both medians!

13 What does the raw data of this FDT look like?

Shoes Frequency 6 12 8 4 10 3 12 8

The Raw data, before it was put into the FDT looked like: 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12

14 From the below FDT, what is the mode?


Refer to the previous question, You can see that the number 6 appears 12 times, more than any other number. Mode = 6



15 This shows how many pairs of shoes students own. How many students were surveyed?


There were 27 students. Look at the previous question, the raw data is a set of 27 numbers. There were 12 students with 6 pairs of shoes, there were 4 students with 8 pairs of shoes etc 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12 27 Students in all!

16 The following data shows the number of children in each household in a suburban street: 2, 2, 3, 2, 3, 4, 3, 1, 3, 2, 3, 3, 4, 1, 1, 2, 2, 2 (a) Display the information in a frequency

table. (b) Display the information as a

histogram/frequency polygon combination graph.

(c) Are you expecting to draw a histogram

in the test? (d) How many people were surveyed?

Answers: (a)

(b)

(c) Yes (d) 18 people were surveyed

17 Some children were surveyed on how much money they get paid for washing the family car. Put the below results into an FDT and then prepare a Histogram and frequency polygon. 4, 5, 6, 7, 5, 8, 5, 6, 4, 5, 7, 5

No. of Children Frequency1 32 73 64 2



18 Data representing the number of pets that a year 8 class has is shown below: 0, 1, 3, 2, 1, 0, 1, 2, 0, 1, 2, 0 What is the mean, median and Range of pets the students have?

1st, put the data into order; 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3 Mean; �̅� = ∑"

#= $%$%$%$%&%&%&%&%'%'%'%(

&'= 1.08

Median, use your fingers to find the Middle number – 1 Range; 𝑥)*" − 𝑥)+# = 3 − 0 = 3 Yes, you need to show your FULL working!

19 Data representing the number of texts our year 8 class receives on their phone for the day could look like; 20, 14, 33, 42, 31, 29, 40, 28, 37 What is the mean, median and range of texts the students receive?

1st, put the data into order; 14, 20, 28, 29, 31, 33, 37, 40, 42 Mean;

�̅� = ∑"#= &,%'$%'-%'.%(&%((%(/%,$%,'

.

= 30.44

Median, use your fingers to find the Middle number – 31 Range; 𝑥)*" − 𝑥)+# = 42 − 14 = 28 Yes, you need to show your FULL working!

20 Paul's batting scores for cricket in a season are 17, 23, 9, 1, 9, 21, 11. Determine Paul’s Mean, Median and Range of batting scores.

Answers: Put into order; 1, 9, 9, 11, 17, 21, 23 Mean ;

�̅� =∑𝑥𝑛

=1 + 9 + 9 + 11 + 17 + 21 + 23

7

= 13 Median = middle number = 11 Mode = most common = 9 Range = 𝑥)*" − 𝑥)+# = 23 − 1 = 22 Yes, you need to show your FULL working!



21 A survey of the number of cars owned by each family in a suburban street gave the following data. 2, 3, 1, 2, 2, 3, 1, 2, 1, 3, 4, 2, 4, 3, 1. (a) What is the mean? (b) Calculate the Median. (c) Determine the mode. (d) Find the Range of the data.

Answers: First, put the data in order: 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4. (a)

𝑀𝑒𝑎𝑛 = �̅� =∑𝑥𝑛

=1 + 1 + 1 + 1 + 2 + 2 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 4 + 4

15

= 2.27 (b)

𝑀𝑒𝑑𝑖𝑎𝑛 =𝑛 + 12 =

15 + 12 = 8𝑡ℎ𝑛𝑢𝑚𝑏𝑒𝑟

Median is 2

(c)

Mode = most common = 2 (d)

𝑅𝑎𝑛𝑔𝑒 = 𝑥)*" − 𝑥)+# = 4 − 1 = 3 Yes, you need to show your FULL working!

22 Is that enough practice? No! I am an engaged, motivated and passionate student, so I will do this worksheet again and then do Worksheet 2 and do some textbook questions again and also do Quizizz multiple times!

worksheet 12.1 representing and interpreting …worksheet 12.1 representing and interpreting data...

Documents