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Statistics, STD1 S1 2020 HSC 2 MC

A random sample of students was taken from each of two universities, and their ages were recorded. The boxplots of their ages are shown.
 

   

For the given samples of students' ages, which of the following statements is FALSE?

  1. The range for University A is smaller than the range for University B.
  2. The median for University A is higher than the median for University B.
  3. The interquartile range (IQR) for University A is larger than the IQR for University B.
  4. The oldest student in the sample from University A is older than the oldest student in the sample from University B.
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`A`

Show Worked Solution

`text{Consider} \ A :`

`text{Range of} \ A \ ≈ 40 – 17.5 ≈ 22.5`

`text{Range of} \ B \ ≈ 30 – 17.5 ≈ 12.5`

`therefore \ text{Range for} \ A > text{Range for}\ B`

`=> A`

Statistics, STD2 S1 2018 HSC 1 MC

A set of scores has the following five-number summary.

lower extreme = 2
lower quartile = 5
median = 6
upper quartile = 8
upper extreme = 9

What is the range?

  1. 2
  2. 3
  3. 6
  4. 7
Show Answers Only

`text(D)`

Show Worked Solution
`text(Range)` `=\ text(upper extreme − lower extreme)`
  `= 9 – 2`
  `= 7`

`=>\ text(D)`

Statistics, STD2 S1 2016 HSC 19 MC

A soccer referee wrote down the number of goals scored in 9 different games during the season.

`2,  \ 3,  \ 3,  \ 3,  \ 5,  \ 5,  \ 8,  \ 9,  \ ...`

The last number has been omitted. The range of the data is 10.

What is the five-number summary for this data set?

  1. `2, 3, 5, 8.5, 12`
  2. `2, 3, 5, 8.5, 10`
  3. `2, 3, 5, 8, 12`
  4. `2, 3, 5, 8, 10`
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`=> A`

Show Worked Solution

`text{Since range is 10} \ => \ text{Last data point = 12}`

`text{Q}_1 = 3`

`text{Q}_3 = (8 + 9)/2 = 8.5`

`text(Median = 5)`

`=> A`

♦ Mean mark 46%.

Statistics, STD2 S1 2004 HSC 6-7 MC

Use the set of scores  1, 3, 3, 3, 4, 5, 7, 7, 12  to answer Questions 6 and 7.
 

Question 6

What is the range of the set of scores?

  1. 6
  2. 9
  3. 11
  4. 12

 

Question 7

What are the median and the mode of the set of scores?

  1. Median 3, mode 5
  2. Median 3, mode 3
  3. Median 4, mode 5
  4. Median 4, mode 3
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`text(Question 6:)\ C`

`text(Question 7:)\ D`

Show Worked Solution

`text(Question 6)`

`text(Range)` `= text(High) – text(Low)`
  `= 12 – 1`
  `= 11`

`=> C`

 

`text(Question 7)`

`text(9 scores)`

`:.\ text(Median)` `= (9 + 1) / 2`
  `=5 text(th score)`
  `= 4`

`text(Mode) = 3`

`=> D`

Statistics, STD2 S1 2007 HSC 21 MC

This set of data is arranged in order from smallest to largest.

 `5, \ 6, \ 11, \ x, \ 13, \ 18, \ 25`

The range is six less than twice the value of  `x`.

Which one of the following is true?

  1.    The median is 12 and the interquartile range is 7.
  2.    The median is 12 and the interquartile range is 12.
  3.    The median is 13 and the interquartile range is 7.
  4.    The median is 13 and the interquartile range is 12.
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`D`

Show Worked Solution

`5, 6, 11, x, 13, 18, 25`

`text(Range)` `= 2x – 6`
`25 – 5` `= 2x – 6`
`2x` `= 26`
`x` `= 13`
`:.\ text(Median)` `= 13`

 
`Q_1 = 6\ \ \ \ \ Q_3 = 18`

`:.\ text(IQR) = 12`

 
`=>  D`

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.)`