Aussie Maths & Science Teachers: Save your time with SmarterEd
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
--- 2 WORK AREA LINES (style=lined) ---
--- 4 WORK AREA LINES (style=lined) ---
i. \(\text{Range}\ = 12.2-7.0 = 5.2 \)
ii. \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 10.4-7.8=2.6 \)
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}
\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 10.4-7.8=2.6 \)
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
--- 2 WORK AREA LINES (style=lined) ---
--- 4 WORK AREA LINES (style=lined) ---
i. \(\text{Median}\ = \dfrac{17+21}{2} = 19 \)
ii. \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 23-14=9 \)
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}
\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 23-14=9 \)
The data set below consists of 8 data points.
\(7.0, \ 7.4, \ 8.1, \ 9.3, \ 9.5, \ 10.7, \ 11.1, \ 12.9 \)
Complete the 5-number summary table of the data set below. (2 marks)
\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} \rule[-1ex]{0pt}{0pt} & \\
\hline
\end{array}
\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} & 7.75 & 9.4 & 10.9 & 12.9 \\
\hline
\end{array}
\(\underbrace{7.0}_{\text{min}}, \underbrace{7.4,\ 8.1}_{Q1}, \ \underbrace{9.3, \ 9.5}_{Q2}, \ \underbrace{10.7, \ 11.1}_{Q3}, \ \underbrace{12.9}_{\text{max}}\)
\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} & 7.75 & 9.4 & 10.9 & 12.9 \\
\hline
\end{array}
Rocket Reddy played 10 full seasons of first grade rugby league and recorded the number of tries he scored each season.
\(13, \ 5, \ 11, \ 2, \ 10, \ 13, \ 5, \ 7, \ 8, \ 3\)
Complete the 5-number summary table of Rocket Reddy's data below. (2 marks)
\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} \rule[-1ex]{0pt}{0pt} & \\
\hline
\end{array}
\(\underbrace{2}_{\text{min}}, \ 3, \underbrace{5}_{Q1}, \ 5, \ \underbrace{7, \ 8}_{Q2}, \ 10, \ \underbrace{11}_{Q3}, \ 13, \ \underbrace{13}_{\text{max}}\)
\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} 2 \rule[-1ex]{0pt}{0pt} & 5 & 7.5 & 11 & 13 \\
\hline
\end{array}
\(\text{Place data points in order:}\)
\(2, \ 3, \ 5, \ 5, \ 7, \ 8, \ 10, \ 11, \ 13, \ 13\)
\(\underbrace{2}_{\text{min}}, \ 3, \underbrace{5}_{Q1}, \ 5, \ \underbrace{7, \ 8}_{Q2}, \ 10, \ \underbrace{11}_{Q3}, \ 13, \ \underbrace{13}_{\text{max}}\)
\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} 2 \rule[-1ex]{0pt}{0pt} & 5 & 7.5 & 11 & 13 \\
\hline
\end{array}
Write down the five-number summary for the dataset
`3, \ 7, \ 8, \ 11, \ 13, \ 18.` (2 marks)
--- 5 WORK AREA LINES (style=lined) ---
| `text(Minimum value:)` | `3` |
| `text(First quartile:)` | `7` |
| `text(Median:)` | `(11 + 8)/2 = 9.5` |
| `text(Third quartile:)` | `13` |
| `text(Maximum value:)` | `18` |
| `text(Minimum value:)` | `3` |
| `text(First quartile:)` | `7` |
| `text(Median:)` | `(11 + 8)/2 = 9.5` |
| `text(Third quartile:)` | `13` |
| `text(Maximum value:)` | `18` |
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?
`=> A`
`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`