worksheet 12.2 representing and interpreting data name: · 2020-05-10 · worksheet 12.2...

© John Wiley & Sons Australia, Ltd 1

WorkSHEET 12.2 Representing and interpreting data

Name: ___________________________ Fluency 1 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 number of pets the students have?

Answer: Mean ;

�̅� = ∑"#= $%&%'%(%&%$%&%(%$%&%(%$

&(

= 1.08

2 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 number of pets the students have, including that new student with 14 pets?

Answer: Mean ;

�̅� = ∑"#= $%&%'%(%&%$%&%(%$%&%(%$%&)

&'

= 2.07

That confirms our answer to earlier in the other worksheet, that including the new student with 14 pets would Increase the mean.

3 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 number of texts the students receive?

Answer: Mean ;

�̅� = ∑"#= ($%&)%''%)(%'&%(*%)$%(+%',

*

= 30.44

4 Data representing the number of texts our yr 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 number of texts the students receive, if we include Mr Finney’s outlier of 2?

Answer: Mean ;

�̅� = ∑"#= ($%&)%''%)(%'&%(*%)$%(+%',%(

&$

= 27.6

That confirms our answer earlier in the other worksheet, that including Mr Finney’s texts would Decrease the mean. *** Notice how I show my full working EVERY time!



5 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

6 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, if we include that outlier of the new student with 14 pets?

1st, put the data into order; 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 14 Mean;

�̅� = ∑"#= $%$%$%$%&%&%&%&%(%(%(%'%&)

&'

= 2.07


7 Have you noticed that maths is about Repetition J

8 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




9 Data representing the number of texts our yr 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, if we include Mr Finney’s outlier of 2?

1st, put the data into order; 2, 14, 20, 28, 29, 31, 33, 37, 40, 42 Mean;

�̅� = ∑"#= (%&)%($%(+%(*%'&%''%',%)$%)(

&$

= 27.6

Median, use your fingers to find the Middle number = 30 Range; 𝑥-." − 𝑥-/# = 42 − 2 = 40

10 Use the frequency distribution table below to answer the following questions.

(a) How many data results were collected? (b) Which score had the highest

frequency?

(c) Which score(s) had the lowest

frequency?

Answers:

(a) Total = 6 + 12 + 9 + 7 + 6 Total = 40

(b) 12 (c) 11 and 15

11 Find the mean of each set of scores. (a) 1.3, 2.4, 5.6, 7.9, 1.2 (b) 7, 6, 5, 10, 2, 4, 8

Answers: (a)

𝑀𝑒𝑎𝑛 = �̅� =∑𝑥𝑛

=1.3 + 2.4 + 5.6 + 7.9 + 1.2

5

= 3.68 (b)


=7 + 6 + 5 + 10 + 2 + 4 + 8

7

= 6

Score Frequency11 0612 1213 0914 0715 06



12 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)


=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



13 Terry obtained the following test results. The scores are out of 10. 7, 8, 9, 5, 7, 6, 8, 4, 8, 7, 7 Determine the Mean, Median, Mode and Range.

Answers: First, put the data in order: 4, 5, 6, 7, 7, 7, 7, 8, 8, 8, 9.


=4 + 5 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 8 + 9

11

= 6.91



Median is 7

Mode = most common = 7

𝑅𝑎𝑛𝑔𝑒 = 𝑥-." − 𝑥-/# = 9 − 4 = 5

14 Twenty young people were picked at random and surveyed to find the number of colours they have in their hair. Here are the raw data collected: 1, 3, 4, 2, 1, 2, 2, 2, 1, 1, 2, 2, 3, 3, 1, 2, 3, 1, 1, 2. (a) Organise the data into a frequency

distribution table.

(b) How many people have 1 colour in their hair?

(c) Which score has the highest

frequency?

Answers: (a)

(b) 7 people (c) 2 colours

15 Are the following statements true or false? The mode of: (a) 1, 2, 3, 4, 4, 5 is 5 (b) 12, 11, 17, 16, 11, 12, 11 is 11.

Answers: (a) False (b) True

Numbers of hair

colours Frequency1 72 83 44 1



16 Are the following statements true or false? The median of: (a) 1, 3, 5, 7, 9 is 5 (b) 9, 15, 7, 12, 7 is 7.

Answers: (a) 1, 3, 5, 7, 9

True

(b) 7, 7, 9, 12, 15

False

17

(a) From the histogram above draw a

frequency distribution table showing days and frequency.

(b) On which day did Joe consume the

least amount of coffee? (c) On which day did he consume 9 cups

of coffee?

Answers: (a)

(b) Monday (c) Friday

Days FrequencyMonday 2Tuesday 4Wednesday 7Thursday 5Friday 9



18 The ages of members of an archery club is shown on the stem plot below. a Determine the Mean, Median and

Range of this data.

Key: 0|4 = 4 kg

Stem Leaf 1 7 8 9 2 3 6 6 6 3 1 1 6 7 8 4 2 2 5 6 5 0 3 6 8

Answers:


=17 + 18 + 19 +⋯+ 53 + 68

19

= 35.74



Median is 36


𝑅𝑎𝑛𝑔𝑒 = 𝑥-." − 𝑥-/# = 68 − 17 = 51

19

(a) What was the most common

temperature for the week? (b) What was the mean average temperature?

Answers: (a) Mode = most common = 31oC (b)


=33 + 31 + 30 + 27 + 32 + 31 + 29

7

= 30.43

20 What is the median temperature for the data in the last question?

Answer: Must put the data into order, then because it’s a small set of data, just use your fingers to find the Middle number; 27, 29, 30, 31, 31, 32, 33 Median temperature is 31°C.

Temperature over the weekDay 1 2 3 4 5 6 7Temp (°C) 33 31 30 27 32 31 29



21 *** Dot Plots are NOT required and won’t be in our test, but they are easy to work out, so its good practice for you to do one. The dotplot below shows the number of games won (out of a possible 20) by the local soccer club over the last 20 seasons.

Find the Mean, Median, Mode and Range of the data.

Answers: First, put the data in order:

7, 3 × 90𝑠, 3 × 100𝑠, 6 × 110𝑠, 4× 120𝑠, 13, 14,15


=7 + 3 × 9 + 3 × 10 + 6 × 11 + 4 × 12 + 13 + 14 + 15

20

= 11


20 + 12 = 10.5𝑡ℎ𝑛𝑢𝑚𝑏𝑒𝑟

the 10th number is 11 and the 11th number is 11, so,

Median is 11


𝑅𝑎𝑛𝑔𝑒 = 𝑥-." − 𝑥-/# = 15 − 7 = 8



22 Key: 2|5 = 25

Use the stem-and-leaf plot above to find the Mean, Median, Mode and Range of the data.

Answers:


=14 + 15 + 20 +⋯+ 52 + 53

16

= 36.6


16 + 12 = 8.5𝑡ℎ𝑛𝑢𝑚𝑏𝑒𝑟


Median is 42.5


𝑅𝑎𝑛𝑔𝑒 = 𝑥-." − 𝑥-/# = 53 − 14 = 39

23

Which boy had the highest mean daily allowance?

Answer: James


=1 + 1 + 1.5 + 2 + 2

5

= $1.50 Chris


=1 + 1.5 + 2.5 + 3 + 3

5

= $2.20 Chris had the highest mean daily allowance.

Stem Leaf1 4 52 0 1 1 23 4 74 8 9 9 95 0 2 2 3

James' daily allowance over 5 days$1 $1.50 $2 $1 $2

Chris' daily allowance over 5 days$3 $1.50 $2.50 $3 $1



24 The table below shows ages of children in a friendship group consisting of five families.

Use the table above to find the Mean, Median, Mode and Range of the data.

Answers: (a)


=17914

= 12.79


14 + 12 = 7.5𝑡ℎ𝑛𝑢𝑚𝑏𝑒𝑟


Median is 13


𝑅𝑎𝑛𝑔𝑒 = 𝑥-." − 𝑥-/# = 15 − 10 = 5 Full working … EVERY time!

Ages of children in five familiesAge Frequency10 211 112 313 214 415 2

Average ages of children in five familiesAge (x ) Frequency (f ) xf

10 02 02011 01 01112 03 03613 02 02614 04 05615 02 030

14 179



25 (b) From the below stem and Leaf plot, calculate the mean and median test scores for each class.

Key: 2|3 = 23 Class 8A Stem Class 8B 2 3 4 3 1 7 7 4 1 7 9 4 5 2 4 6 9 6 3 0 6 0 2 2 3 6 8 9 8 8 7 3 7 0 2 2 5 7 9 9 8 6 5 3 2 0 8 1 8 1 0 9 (c) Calculate the range for each class.

(b) Class 8A: Total = 1611

Mean =

= 73.2 With 22 values, choose the average of the 11th and 12th values. Median = 78 Class 8B: Total = 1336

Mean =

= 60.7 With 22 values, choose the average of the 11th and 12th values.

Median =

= 62.5 (c) Class 8A: range = 91 – 34 = 57

Class 8B: range = 88 – 23 = 65

26

Are the following statements true or false? (a) There are 30 pieces of data. (b) The most common frequency is 5. (c) The score with a frequency of 15 is 6.

Answers: (a) Total = 3 + 0 + 7 + 11 + 2 + 15

Total = 38 (False) Total (b) False … the most common frequency is 15 (c) True

161122

133622

62 632+

Score Frequency3.5 030.4 004.5 070.5 115.5 020.6 15



27 The number of goals scored in soccer matches in an international tournament is tabled below:

Determine the Mean, Media, Mode and Range of this data.

Mean:

�̅� =∑𝑥𝑛

=10148

= 2.1

Median:

𝑛 + 12 =

48 + 12 = 24.5𝑡ℎ𝑛𝑢𝑚𝑏𝑒𝑟

24th no. is a 2 … 25th no. is a 2 Median = 2 Mode: Most common … Mode =1 Range:

𝑥-." − 𝑥-/# = 7 − 0 = 7



28 Determine the Mean, Median, Mode and range of:

Mean:

�̅� =∑𝑥𝑛

=0 × 2 + 1 × 5 + 2 × 12 + 3 × 10 + 4 × 7 + 5 × 2

38

=9738

= 2.55

Median:

𝑛 + 12 =

38 + 12 = 19.5𝑡ℎ𝑛𝑢𝑚𝑏𝑒𝑟

19th no. is 2 … 20th no. is 3 Median = 2.5 Mode: Most common … Mode =2 Range:

𝑥-." − 𝑥-/# = 5 − 0 = 5



29 Determine the mean, median, Mode and Range for:

Mean:

�̅� =∑𝑥𝑛

=3 × 19 + 4 × 53 + 5 × 21 + 6 × 4 + 7 × 2 + 8 × 1

100

=420100

= 4.2

Median:

𝑛 + 12 =

100 + 12 = 50.5𝑡ℎ𝑛𝑢𝑚𝑏𝑒𝑟

50th no. is 4 … 51st no. is 4 Median = 4 Mode: Most common … Mode =4 Range:

𝑥-." − 𝑥-/# = 8 − 3 = 5

30 The amount ($) given to 12-year-olds for washing the family car is described by this histogram.

Determine the Mean, Median and Range for this data:

Answer: The raw data looks like: 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 8. Mean = ∑"

#= )%)%1%1%1%1%1%2%2%,%,%+

&(=

5.58 Median = middle number = 5 Range = 𝑥-." − 𝑥-/# = 8 − 4 = 4

worksheet 12.2 representing and interpreting data name: · 2020-05-10 · worksheet 12.2...

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