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Data Analysis, SM-Bank 047 MC

Angelica made a dot plot to show the distances she has run in her training for a marathon.
 

 
What is the range of the distances Angelica has run?

  1. \(3\)
  2. \(7\)
  3. \(21\)
  4. \(24\)
Show Answers Only

\(B\)

Show Worked Solution
\(\text{Range}\ \) \(=\ \text{high – low}\)
  \(=25-1\)
  \(=7\)

\(\Rightarrow B\)

Data Analysis, SM-Bank 035

A data set has a range of 50 and a mean of 20.

Give an example of a dataset using 4 numbers that satisfies this condition.  (2 marks)

Show Answers Only

`0,  10,  20,  50`

`text(Note: other answers are possible.)`

Show Worked Solution

`0,  10,  20,  50`

`text(Range) = 50 \ -\ 0 = 50`

`text(Sum of the numbers) = 20 xx 4 = 80`

`text(Mean) = (0 + 10 + 20 +50)/4\ = 80/4 \= 20`

`text(Note: other answers are possible.)`

Data Analysis, SM-Bank 028

Find the range for this set of scores.  (1 mark)

`74, \ 89, \ 65, \ 64, \ 87, \ 88, \ 68, \ 74, \ 72`

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`25`

Show Worked Solution

`text(Range) = text(Highest score) \-\text(Lowest score)   = 89 \-\64 = 25`

Data Analysis, SM-Bank 020

An AFL team has 10 players with the following heights in centimetres.

`180, \ 175, \ 163, \ 192, \ 200, \ 193, \ 195, \ 195, \ 188, \ 195`

What is the range of heights?  (1 mark)

Show Answers Only

`37\ text(centimetres)`

Show Worked Solution
`text(Range)` `=  200\-\163`
  `=  37\ text(centimetres)`

Data Analysis, SM-Bank 015

A policeman is recording the speed of 25 cars travelling on a highway using a speed gun.

The results are shown in the stem-and-leaf plot.

  1. What is the median speed?  (1 mark)

  2. What is the range of the speeds?  (1 mark)

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a.   `119\ text(km/hr)`

b.  `49\ text(km/hr)`

Show Worked Solution

a.   `25\ text(data points)`

`text(Median is the 13th data point)`

`:.\ text(Median) = 119\ text(km/hr)`
 

b.   `text(Range)` `= text(Highest) \ – \ text(Lowest)`
    `= 139\ – \ 90`
    `=49\ text(km/hr)`

 

Data Analysis, SM-Bank 003

This table shows the number of people who visited a war memorial on weekdays over 4 weeks.
 

 
 

  1. What was the range of people visiting the war memorial on Monday?  (1 mark)

  2. What was the mean number of people who attended the war memorial on Fridays?  (1 mark)

  3. What was the median number of people who visited the war memorial during week 3?  (1 mark)

  4. What is the modal number of visitors to the war memorial during the four week period?  (1 mark)

Show Answers Only

a.   `44`

b.   `26`

c.   `39`

d.   `22`

Show Worked Solution
a.   `text(Range on Mondays)` `= 81 \ -\ 37`
  `= 44`

 

b.   `text(Mean on Fridays)` `=(22 + 32+28+22)/4`
  `=104/4`
  `=26`

  
c.   `text(Week 3 data in order:   28,  37,  39,  53,  72)`

`text(Median Week 3)` `=\ text(middle score)`
  `=\  39`

 
d.   `text(Modal number of visitors) = 22`

Statistics, STD2 S1 2008 HSC 3 MC

The stem-and-leaf plot represents the daily sales of soft drink from a vending machine.

If the range of sales is 43, what is the value of  2008 3 mc  ?

 
 

  1.    `4` 
  2.    `5`
  3.    `24`
  4.    `25`
Show Answers Only

`A`

Show Worked Solution

`text(Range = High) – text(Low) = 43`

`:.\ 67 – text(Low)` `= 43`
`text(Low)` `= 24`

`:.\ N = 4`

`=>  A`

Statistics, STD2 S1 2013 HSC 26b

Write down a set of six data values that has a range of 12, a mode of 12 and a minimum value of 12.   (2 marks)

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 `12, 12, 12, 16, 18, 24`

Show Worked Solution

`12, 12, 12, 16, 18, 24`

`text(NB. There are many correct solutions.)`

 

Statistics, STD2 S1 2010 HSC 1 MC

The results of a survey are displayed in the dot plot.

What is the range of this data?
 

2010 1 MC 
 

  1.    7
  2.    8
  3.    9
  4.    10
Show Answers Only

`C`

Show Worked Solution
`text(Range)` `=text(High)-text(Low)`
  `=9-0`
  `=9`

`=>  C`