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Box Plots and 5-Number, SM-Bank 011

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

  1. the range   (1 mark)

  2. the interquartile range   (2 marks)

Show Answers Only

i.   \(\text{Range}\ = 7 \)

ii.   \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 6-1=5 \)

Show Worked Solution

i.   \(\text{Range}\ = 7-0=7 \)
  

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 & 4 & 6 & 7 \\
\hline
\end{array}

\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 6-1=5 \)

Box Plots and 5-Number, SM-Bank 009

Yoyo was practicing his cello for an orchestra audition and the data set below records the number of hours he practiced each day over a 10-day period.

\(7.6, \ 12.2, \ 8.4, \ 7.8, \ 8.8, \ 9.3, \ 11.9, \ 7.0, \ 8.2, \ 10.4\)

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

  1. the range   (1 mark)

  2. the interquartile range   (2 marks)

Show Answers Only

i.    \(\text{Range}\ = 12.2-7.0 = 5.2 \)
 

ii.   \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 10.4-7.8=2.6 \)

Show Worked Solution

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

\(7.0, \ 7.6, \ 7.8, \ 8.2, \ 8.4, \ 8.8, \ 9.3, \ 10.4, \ 11.9, \ 12.2\)

\(\text{Range}\ = 12.2-7.0 = 5.2 \)
 

ii.    \(\underbrace{7.0}_{\text{min}}, \ 7.7, \ \underbrace{7.8}_{Q1}, \ 8.2, \ \underbrace{8.4, \ 8.8}_{Q2}, \ 9.3, \ \underbrace{10.4}_{Q3}, \ 11.9, \ \underbrace{12.2}_{\text{max}}\)

\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}  7.0 \rule[-1ex]{0pt}{0pt} & 7.8 & 8.6 & 10.4 & 12.2 \\
\hline
\end{array}

\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 10.4-7.8=2.6 \)

Box Plots and 5-Number, SM-Bank 004

Robert records the total goals scored in each of the first 11 matches of his favourite soccer team.

\(3, \ 5, \ 1, \ 2, \ 2, \ 7, \ 6, \ 4, \ 1, \ 5, \ 3\)

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

  1. the range   (1 mark)

  2. the interquartile range   (2 marks)

Show Answers Only

i.    \(\text{Range}\ = 7-1=6\)

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

Show Worked Solution

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

\(1, \ 1, \ 2, \ 2, \ 3, \ 3, \ 4, \ 5, \ 5, \ 6, \ 7\)

\(\text{Range}\ = 7-1=6\)
 

ii.   \(\underbrace{1}_{\text{min}}, 1, \ \underbrace{2}_{Q1}, \ 2, \ 3, \ \underbrace{3}_{Q2}, \ 4, \ 5, \ \underbrace{5}_{Q3}, \ 6, \ \underbrace{7}_{\text{max}}\)

\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}  1 \rule[-1ex]{0pt}{0pt} & 2 & 3 & 5 & 7 \\
\hline
\end{array}

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

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
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 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%.