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Box Plots and 5-Number, SM-Bank 010

Using a 5-number summary of the data represented in this graph, or otherwise, determine

  1. the median   (1 mark)

  2. the interquartile range   (2 marks)

Show Answers Only

i.   \(\text{Median}\ = 2 \)

ii.   \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 5-1=4 \)

Show Worked Solution

i.   \(\text{15 data points}\ \Rightarrow \ \text{Median = 8th data point}\)

\(\text{Median}\ = 2 \)
  

ii.   
           

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  0 \rule[-1ex]{0pt}{0pt} & 1 & 2 & 5 & 7 \\
\hline
\end{array}

\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 5-1=4 \)

Box Plots and 5-Number, SM-Bank 008

Matt records the number of times he takes his dog Max for a walk each month. The data set below records the months January to August.

\(21, \ 24, \ 28, \ 22, \ 15, \ 12, \ 13, \ 17\)

Using a 5-number summary of this dataset, or otherwise, determine

  1. the median   (1 mark)

  2. the interquartile range   (2 marks)

Show Answers Only

i.    \(\text{Median}\ = \dfrac{17+21}{2} = 19 \)
 

ii.    \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 23-14=9 \)

Show Worked Solution

i.    \(\text{Placing data values in order:}\)

\(12, \ 13, \ 15, \ 17, \ 21, \ 22, \ 24, \ 28 \)

\(\text{Median}\ = \dfrac{17+21}{2} = 19 \)
 

ii.    \(\underbrace{12}_{\text{min}}, \underbrace{13+15}_{Q1}, \ \underbrace{17+21}_{Q2}, \ \underbrace{22, \ 24}_{Q3}, \ \underbrace{28}_{\text{max}}\)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  12 \rule[-1ex]{0pt}{0pt} & 14 & 19 & 23 & 28 \\
\hline
\end{array}

\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 23-14=9 \)

Box Plots and 5-Number, SM-Bank 005

Le Bron plays basketball and records the number of free throws he shoots in the first nine games of the season.

\(12, \ 8, \ 4, \ 15, \ 13, \ 7, \ 8, \ 3, \ 10\)

Using a 5-number summary of this dataset, or otherwise, determine

  1. the median   (1 mark)

  2. the interquartile range   (2 marks)

Show Answers Only

i.    \(\text{Median}\ = 8\)

ii.    \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 5-2 =3\)

Show Worked Solution

i.    \(\text{Ordering the data values:}\)

\(3, \ 4, \ 7, \ 8, \ 8, \ 10, \ 12, \ 13, \ 15\)

\(\text{Median}\ = 8\)
 

ii.    \(\underbrace{3}_{\text{min}}, \ \underbrace{4, \ 7}_{Q1}, \ 8, \ \underbrace{8}_{Q2}, \ 10, \ \underbrace{12, \ 13}_{Q3}, \ \underbrace{15}_{\text{max}}\)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  3 \rule[-1ex]{0pt}{0pt} & 5.5 & 8 & 12.5 & 15 \\
\hline
\end{array}

\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 12.5-5.5 =7\)

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 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%.