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Statistics, STD2 S1 2015 HSC 29d*

Data from 200 recent house sales are grouped into class intervals and a cumulative frequency histogram is drawn.
 

2UG 2015 29d1 

  1. Use the graph to estimate the median house price.   (1 mark)

  2. By completing the table, identify the modal class interval for the house price data.   (2 marks)

\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}

Show Answers Only
a.   

2UG 2015 29d Answer

`text(From the graph, the estimated median house price = $392 500)`

b.

\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{Modal class interval}\ = $390\ 000-$400\ 000\  (\text{or}\ $395\ 000)`

Show Worked Solution
a.   

2UG 2015 29d Answer

`text(From the graph, the estimated median house price = $392 500)`

b.

\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{Modal class interval}\ = $390\ 000-$400\ 000\  (\text{or}\ $395\ 000)`

Statistics, STD2 S1 2010 HSC 26b*

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.
 

2010 26b

  1. Find the value of  Χ  in the table.   (1 mark)

  2. On the cumulative frequency histogram above, draw a cumulative frequency polygon (ogive) for this data.   (1 mark)
  3. Use your graph to determine the median. Show, by drawing lines on your graph, how you arrived at your answer.   (1 mark)
Show Answers Only

a.    `15`

b. & c.
               

`text(Median)\ ~~155`

Show Worked Solution

a.    `X= 25-10= 15`

b. & c.
               

`text(Median)\ ~~155`

Statistics, STD2 S1 2014 HSC 26e

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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Show Worked Solution
♦♦♦ Mean mark 17%.

HSC 2014 26ei

Statistics, STD2 S1 2011 HSC 11 MC

The sets of data, `X` and `Y`, are displayed in the histograms.

2UG 2011 11

Which of these statements is true?

  1. `X` has a larger mode and `Y ` has a larger range.
  2. `X` has a larger mode and the ranges are the same.
  3. The modes are the same and `Y` has a larger range.
  4. The modes are the same and the ranges are the same.
Show Answers Only

`B`

Show Worked Solution
♦ Mean mark 47%

`text(Mode of)\ X=9`

`text(Range of)\ X=9-3=6`

`text(Mode of)\ Y=8`

`text(Range of)\ Y=11-5=6`

`:. X\ text(has a larger mode and ranges are the same)`

`=>B`