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Statistics, STD2 EQ-Bank 3 MC

For the data below, which is the correct five figure summary?

\(12,\ \ 16, \ \ 4,\ \ 6, \ \ 4, \ \ 5, \ \  22, \ \ 20, \ \ 12, \ 8\ \)

  1. \(4,\ \ 5, \ \ 8,\ \ 16, \ \ 21\)
  2. \(4,\ \ 5, \ \ 8,\ \ 16, \ \ 22\)
  3. \(4,\ \ 5, \ \ 10,\ \ 16, \ \ 21\)
  4. \(4,\ \ 5, \ \ 10,\ \ 16, \ \ 22\)
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Ordered data set}\ \rightarrow\ \ 4,\ \ 4, \ \ 5,\ \ 6, \ \ 8, \ \ 12, \ \  12, \ \ 16, \ \ 20, \ 22\ \)

\(\text{Five number Summary}\)

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \text{Minimum} \rule[-1ex]{0pt}{0pt} &  4\\
\hline
\rule{0pt}{2.5ex} \ Q_1 \rule[-1ex]{0pt}{0pt} & 5 \\
\hline
\rule{0pt}{2.5ex} \text{Median} \rule[-1ex]{0pt}{0pt} &  \dfrac{8+12}{2}=10\\
\hline
\rule{0pt}{2.5ex} \ Q_3 \rule[-1ex]{0pt}{0pt} & 16 \\
\hline
\rule{0pt}{2.5ex} \text{Maximum} \rule[-1ex]{0pt}{0pt} &  22\\
\hline
\end{array}

\(\Rightarrow D\)

Statistics, STD2 EQ-Bank 5 MC

The results of a test are displayed in the box-and-whisker plot below.
 

Which of the following statements is false?

  1. The median is 155
  2. The range is 60
  3. The interquartile range is 50
  4. 25% of the scores are below 150
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Five number Summary}\)

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \text{Minimum} \rule[-1ex]{0pt}{0pt} &  140\\
\hline
\rule{0pt}{2.5ex} \ Q_1 \rule[-1ex]{0pt}{0pt} & 150 \\
\hline
\rule{0pt}{2.5ex} \text{Median} \rule[-1ex]{0pt}{0pt} &  155\\
\hline
\rule{0pt}{2.5ex} \ Q_3 \rule[-1ex]{0pt}{0pt} & 190 \\
\hline
\rule{0pt}{2.5ex} \text{Maximum} \rule[-1ex]{0pt}{0pt} &  200\\
\hline
\end{array}

\(\text{Median}\ =\ 155\ \checkmark\)

\(\text{Range}\ =\ 200-140=60\ \checkmark\)

\(\text{IQR}\ =\ 190-150=40\ \text{not}\ 50\ \)X

\(\text{Q1}\ =\ 150\ \therefore\ 25\%\ \text{of scores lie below 150}\ \checkmark\)

\(\Rightarrow C\)

Statistics, STD2 EQ-Bank 17

A Physics class of  12 students is going on a 4 day excursion by bus.

The students are asked to each pack one bag for the trip. The bags are weighed, and the weights (in kg) are listed in order as follows:

\(8,\ \ 9, \ \ 10,\ \ 10, \ \ 15, \ \  18, \ \  22, \ \ 25, \ \ 29, \ \ 35, \ \ 38, \ \ 41 \)

  1. Use the above data to produce a five number summary for the weights of the bags.   (2 marks)
  3. Using your five number summary from part (a), calculate the interquartile range of the weights.   (2 marks)
Show Answers Only

a.    \(\text{Five number Summary}\)

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \text{Minimum} \rule[-1ex]{0pt}{0pt} &  8\\
\hline
\rule{0pt}{2.5ex} \ Q_1 \rule[-1ex]{0pt}{0pt} & 10 \\
\hline
\rule{0pt}{2.5ex} \text{Median} \rule[-1ex]{0pt}{0pt} &  20\\
\hline
\rule{0pt}{2.5ex} \ Q_3 \rule[-1ex]{0pt}{0pt} & 32 \\
\hline
\rule{0pt}{2.5ex} \text{Maximum} \rule[-1ex]{0pt}{0pt} &  41\\
\hline
\end{array}

b.     \(22\)

Show Worked Solution

a.    \(\text{Five number Summary}\)

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \text{Minimum} \rule[-1ex]{0pt}{0pt} &  8\\
\hline
\rule{0pt}{2.5ex} \ Q_1 \rule[-1ex]{0pt}{0pt} & 10 \\
\hline
\rule{0pt}{2.5ex} \text{Median} \rule[-1ex]{0pt}{0pt} &  20\\
\hline
\rule{0pt}{2.5ex} \ Q_3 \rule[-1ex]{0pt}{0pt} & 32 \\
\hline
\rule{0pt}{2.5ex} \text{Maximum} \rule[-1ex]{0pt}{0pt} &  41\\
\hline
\end{array}

b.     \(\text{IQR}\) \(=Q_3-Q_1\)
    \(=32-10=22\)

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.
Show Answers Only

`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 EQ-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
Show Answers Only

`D`

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

 
`=> D`

Statistics, STD2 S1 EQ-Bank 22

Write down the five-number summary for the dataset 

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

Show Answers Only
`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 2017 HSC 1 MC

The box-and-whisker plot for a set of data is shown.
 

What is the median of this set of data?

  1. 15
  2. 20
  3. 30
  4. 35
Show Answers Only

`C`

Show Worked Solution

`text(Median = 30)`

`=> C`

Statistics, STD2 S1 2016 HSC 22 MC

The box-and-whisker plots show the results of a History test and a Geography test.
 

In History, 112 students completed the test. The number of students who scored above 30 marks was the same for the History test and the Geography test.

How many students completed the Geography test?

  1. 8
  2. 50
  3. 56
  4. 112
Show Answers Only

`=> C`

Show Worked Solution

`text{In History} \ => \  text{Q}_3 = 30\ \text{marks}`

`:.\ text{Scoring over 30}\ = 25text(%) xx 112 = 28\ \text{students}`
 

`text{In Geography} \ => \ text{Median}\ = 30\ \text{marks}`

`:.\ text{Students completing Geography}\ =2 xx 28 = 56\ \text{students}`

`=> C`

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`
Show Answers Only

`=> 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%
Show Answers Only

`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
Show Answers Only

`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 2008 HSC 10 MC

The marks for a Science test and a Mathematics test are presented in box-and-whisker plots.
 

 Which measure must be the same for both tests?

  1. Mean
  2. Range
  3. Median
  4. Interquartile range
Show Answers Only

`D`

Show Worked Solution

`text(IQR)=text(Upper Quartile)-text(Lower Quartile)`

`text{In both box plots, IQR = 3 intervals (against bottom scale)}`

`=>  D`

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
Show Answers Only

`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%.