Aussie Maths & Science Teachers: Save your time with SmarterEd
The heights of students in a class were recorded.
The results for this class are displayed in the cumulative frequency graph shown.
The shortest student in this class is 130 cm and the tallest student is 180 cm.
Construct a box-plot for this class in the space below. (3 marks)
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\(Q_1(7.5 \ \text{students })=135\)
\(Q_3(22.5 \ \text{students })=160\)
\(\text{Median (15 students )}=140\)
The cumulative frequency graph shows the distribution of the number of movie downloads made by 100 people in one month.
Which box-plot best represents the same data as displayed in the cumulative frequency graph?
`text{1st quartile}\ ~~ 3`
`text{Median}\ ~~ 6`
`text{3rd quartile}\ ~~ 7`
`=>C`
The number of downloads of a song on each of twenty consecutive days is shown in the following graph.
Which of the following graphs best shows the cumulative number of downloads up to and including each day?
Which histogram best represents a dataset that is positively skewed?
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The graph displays the mean monthly rainfall in Sydney and Perth.
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The heights of 400 students were measured. The results are displayed in this cumulative frequency polygon.
Use the polygon to estimate the interquartile range. (2 marks)
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`text(See graph for values:)`
| `IQR` | `= Q_3 – Q_1` |
| `= 172 – 136` | |
| `= 36\ text(cm)` |
Data from 200 recent house sales are grouped into class intervals and a cumulative frequency histogram is drawn.
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\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \text{Class Centre} \rule[-1ex]{0pt}{0pt} & \text{Frequency} \\ \text{(\$'000)} & \\
\hline
\rule{0pt}{2.5ex} \rule[-1ex]{0pt}{0pt} & \\
\hline
\rule{0pt}{2.5ex} \rule[-1ex]{0pt}{0pt} & \\
\hline
\rule{0pt}{2.5ex} \rule[-1ex]{0pt}{0pt} & \\
\hline
\rule{0pt}{2.5ex} \rule[-1ex]{0pt}{0pt} & \\
\hline
\end{array}
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| i. |
|
`text(From the graph, the estimated median)`
`text(house price = $392 500)`
ii.
\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \text{Class Centre} \rule[-1ex]{0pt}{0pt} & \text{Frequency} \\ \text{(\$’000)} & \\
\hline
\rule{0pt}{2.5ex} 375 \rule[-1ex]{0pt}{0pt} & 30\\
\hline
\rule{0pt}{2.5ex} 385 \rule[-1ex]{0pt}{0pt} & 50 \\
\hline
\rule{0pt}{2.5ex} 395 \rule[-1ex]{0pt}{0pt} & 70 \\
\hline
\rule{0pt}{2.5ex} 405 \rule[-1ex]{0pt}{0pt} & 50 \\
\hline
\end{array}
`text(Mean house price ($’000))`
`= (375xx30 + 385xx50 + 395xx70 + 405xx50)/200`
`=$392`
`:. text(Mean house price is)\ $392\ 000`
A set of examination results is displayed in a cumulative frequency histogram and polygon (ogive).
Sanath knows that his examination mark is in the 4th decile.
Which of the following could have been Sanath’s examination mark?
`text(4th decile occurs when cumulative frequency)`
`text(is between 15 and 20.)`
`:.\ text(Examination mark must be between 55 and 60.)`
`=> B`
The heights of the 60 members of a choir were recorded. These results were grouped and then displayed as a cumulative frequency histogram and polygon.
The shortest person in the choir is 140 cm and the tallest is 190 cm.
Draw an accurate box-and-whisker plot to represent the data. (3 marks)
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`text(Low) = 140`
`text(High) = 190`
`text(Median) = 150\ \ \ \ text{(# People = 30)}`
`Q_1 = 145\ \ \ \ text{(# People = 15)}`
`Q_3 = 170\ \ \ \ text{(# People = 45)}`
`text(Box and Whisker)`
List TWO ways in which this graph is misleading. (2 marks)
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The sector graph shows the proportion of people, as a percentage, living in each region of Sumcity. There are 24 000 people living in the Eastern Suburbs.
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Jake used the information above to draw a column graph.
Identify this region and justify your answer. (2 marks)
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A set of data is represented by the cumulative frequency histogram and ogive.
What is the best approximation for the interquartile range for this set of data?
| `IQR` | `= Q3 − Q1` |
| `= 80 − 45` | |
| `= 35` |
`=> C`
The graph shows the predicted population age distribution in Australia in 2008.
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The times taken for 160 music downloads were recorded, grouped into classes and then displayed using the cumulative frequency histogram shown.
On the diagram, draw the lines that are needed to find the median download time. (2 marks)
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The graph below displays data collected at a school on the number of students
in each Year group, who own a mobile phone.
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Which student is more likely to own a mobile phone?
Justify your answer with suitable calculations. (2 marks)
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A new shopping centre has opened near a primary school. A survey is conducted to determine the number of motor vehicles that pass the school each afternoon between 2.30 pm and 4.00 pm.
The results for 60 days have been recorded in the table and are displayed in the cumulative frequency histogram.
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What problem could arise from the change in the median number of motor vehicles passing the school before and after the opening of the new shopping centre?
Briefly recommend a solution to this problem. (2 marks)
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`text(Solutions)`
| i. | `X` | `= 25\ -10` |
| `= 15` |
| ii. | |
iii. `text(Median)\ ~~155`
| iv. | `text(Problems)` |
| `text(- increased traffic delays)` | |
| `text(- increased danger to students leaving school)` | |
| `text(Solutions)` | |
| `text(- signpost alternative routes around school)` | |
| `text(- decrease the speed limit in the area)` |
A retailer has collected data on the number of televisions that he sold each week in 2012.
He grouped the data into classes and displayed the data using a cumulative frequency histogram and polygon (ogive).
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Is he correct? Give a reason for your answer. (1 mark)
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On Saturday, Jonty recorded the colour of T-shirts worn by the people at his gym. The results are shown in the graph.
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The sets of data, `X` and `Y`, are displayed in the histograms.
Which of these statements is true?
Which of the following frequency histograms shows data that could be normally distributed?
The frequency histogram shows the number of goals scored by a football team in each game in a season.
What is the mean number of goals scored per game by this team?
A survey was conducted where people were asked which of two brands of smartphones they preferred. The results were:
A graph displaying the data is to be included in a magazine article. The editor of the magazine wishes to ensure that the graph is not misleading in any way.
Which graph should the editor choose to include in the article?
