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Statistics, STD2 S1 SM-Bank 2 MC

A dataset has the following five-number summary.

If the range of the dataset is 8, what is the minimum value of the dataset?

  1.  2
  2.  3
  3.  4
  4.  7
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`D`

Show Worked Solution
`text(Range)` `=\ text{Max}-text{Min}`
`8` `= 15-text{Min Value}`
`:.\ text{Min}` `= 15-8`
  `=7`

 
`=> D`

Statistics, STD2 S1 SM-Bank 1

Write down the five-number summary for the dataset 

`3, \ 7, \ 8, \ 11, \ 13, \ 18.`  (2 marks)

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`text(Minimum value:)`   `3`
`text(First quartile:)`   `7`
`text(Median:)`   `(11 + 8)/2 = 9.5`
`text(Third quartile:)`   `13`
`text(Maximum value:)`   `18`
Show Worked Solution
`text(Minimum value:)`   `3`
`text(First quartile:)`   `7`
`text(Median:)`   `(11 + 8)/2 = 9.5`
`text(Third quartile:)`   `13`
`text(Maximum value:)`   `18`

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 2015 HSC 6 MC

The times, in minutes, that a large group of students spend on exercise per day are presented in the box‑and‑whisker plot.
 

What percentage of these students spend between 40 minutes and 60 minutes per day on exercise?

  1. 17%
  2. 20%
  3. 25%
  4. 50%
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`C`

Show Worked Solution

`text{Q}_1 = 40, \ text(Median) = 60`

`:.\ text(% Students between 40 and 60)`

`= 50text{%}-25text{%}`

`=25 text{%}`
 

`=>C`

Statistics, STD2 S1 2004 HSC 12 MC

This box-and-whisker plot represents a set of scores.
 

What is the interquartile range of this set of scores?

  1. 1
  2. 2
  3. 3
  4. 5
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`C`

Show Worked Solution

`text{Q}_1 = 8, \ text{Q}_3 = 11`

`text{IQR}` `= text{Q}_3-text{Q}_1`
  `= 11-8`
  `= 3`

 
`=> C`

Statistics, STD2 S1 2011 HSC 7 MC

A set of data is displayed in this box-and-whisker plot.
 

Which of the following best describes this set of data?

  1. Symmetrical
  2. Positively skewed
  3. Negatively skewed
  4. Normally distributed
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`B`

Show Worked Solution

`text{Since the median (155) is closer to the lower quartile (150) and range}`

`text{low (140) than the upper quartile (190) and range high (200), it is}`

`text{positively skewed.}`

`=>B`

♦ Mean mark 47%.