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Statistics, STD2 EQ-Bank 11 MC

Twenty-five people were surveyed about the amount of money they spent on groceries per week, to the nearest dollar.

The results are shown in the frequency table.

\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \textit{Amount Spent}  ($) \rule[-1ex]{0pt}{0pt} & \ \ \ \ \ \textit{Frequency}\ \ \ \ \  \\
\hline
\rule{0pt}{2.5ex} 50-99 \rule[-1ex]{0pt}{0pt} & 8 \\
\hline
\rule{0pt}{2.5ex} 100-149 \rule[-1ex]{0pt}{0pt} & 10 \\
\hline
\rule{0pt}{2.5ex} 150-199 \rule[-1ex]{0pt}{0pt} & 7 \\
\hline
\rule{0pt}{2.5ex} 200-249 \rule[-1ex]{0pt}{0pt} & 5 \\
\hline
\end{array}

What is the mean amount spent on groceries by these people per week?

  1. $143.50
  2. $148.50
  3. $153.50
  4. $158.50
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Using the class centres}\)

\(\text{Class centres: } 74.5, 124.5, 174.5, 224.5\)

\(\text{Total hours}\) \(=(74.5 \times 4) + (124.5 \times 9) + (174.5 \times 8) + (224.5 \times 4)\)
  \(=298 + 1120.5 + 1396 + 898\)
  \(=3712.5\)
\(\text{Mean amount}\) \(=\dfrac{3712.5}{25} =$148.50\)

\(\Rightarrow B\)

Statistics, STD2 EQ-Bank 10 MC

Thirty students were surveyed about the number of hours they spent on homework per week, to the nearest hour.

The results are shown in the frequency table.

\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \textit{Hours per week} \rule[-1ex]{0pt}{0pt} & \ \ \ \ \ \textit{Frequency}\ \ \ \ \  \\
\hline
\rule{0pt}{2.5ex} 0-4 \rule[-1ex]{0pt}{0pt} & 8 \\
\hline
\rule{0pt}{2.5ex} 5-9 \rule[-1ex]{0pt}{0pt} & 10 \\
\hline
\rule{0pt}{2.5ex} 10-14 \rule[-1ex]{0pt}{0pt} & 7 \\
\hline
\rule{0pt}{2.5ex} 15-19 \rule[-1ex]{0pt}{0pt} & 5 \\
\hline
\end{array}

What is the mean number of hours of homework completed by the students per week?

  1. 8.0
  2. 8.5
  3. 9.0
  4. 9.5
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Using the class centres}\)

\(\text{Class centres: } 2, 7, 12, 17\)

\(\text{Total hours}\) \(=(2\times 8) + (7\times 10) + (12\times 7) + (17\times 5)\)
  \(=16 + 70 + 84 + 85\)
  \(=255\)
\(\text{Mean hours}\) \(=\dfrac{255}{30} =8.5\)

\(\Rightarrow B\)

Statistics, STD2 S1 2006 HSC 23c*

Vicki wants to investigate the number of hours spent on homework by students at her high school.

She asks each student how many hours (to the nearest hour) they usually spend on homework during one week. 

The responses are shown in the frequency table.

\begin{array} {|c|c|}
\hline
\textit{  Number of hours spent  } & \ \ \ \ \ \textit{Frequency}\ \ \ \ \  \\ \textit{  on homework in a week  } & \\
\hline
\rule{0pt}{2.5ex} \text{0 to 4} \rule[-1ex]{0pt}{0pt} & 69 \\
\hline
\rule{0pt}{2.5ex} \text{5 to 9} \rule[-1ex]{0pt}{0pt} & 72 \\
\hline
\rule{0pt}{2.5ex} \text{10 to 14} \rule[-1ex]{0pt}{0pt} & 38 \\
\hline
\rule{0pt}{2.5ex} \text{15 to 19} \rule[-1ex]{0pt}{0pt} & 21 \\
\hline
\end{array}

What is the mean amount of time spent on homework?   (2 marks)

Show Answers Only

`text(7.275 hours)`

Show Worked Solution

MARKER’S COMMENT: This “routine” exercise of finding a mean from grouped data was incorrectly answered by most students! The best responses copied the table and inserted a class-centre column (see solution).
      2UG-2006-23c Answer

 

`text(Mean)` `= text(Sum of Scores) / text(Total scores)`
  `= 1455/200`
  `= 7.275\ text(hours)`

Statistics, STD2 S1 2016 HSC 21 MC

A grouped data frequency table is shown.

\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \textit{Class Interval} \rule[-1ex]{0pt}{0pt} & \ \ \ \ \ \textit{Frequency}\ \ \ \ \  \\
\hline
\rule{0pt}{2.5ex} \text{1 – 5} \rule[-1ex]{0pt}{0pt} & 3 \\
\hline
\rule{0pt}{2.5ex} \text{6 – 10} \rule[-1ex]{0pt}{0pt} & 6 \\
\hline
\rule{0pt}{2.5ex} \text{11 – 15} \rule[-1ex]{0pt}{0pt} & 8 \\
\hline
\rule{0pt}{2.5ex} \text{16 – 20} \rule[-1ex]{0pt}{0pt} & 9 \\
\hline
\end{array}

What is the mean for this set of data?

  1.    6.5
  2.    10.5
  3.    11.9
  4.    12.4
Show Answers Only

`=> D`

Show Worked Solution

`text(Using the centre of each class interval:)`

♦ Mean mark 43%.
`text(Mean)` `= (3 xx 3 + 8 xx 6 + 13 xx 8 + 18 xx 9)/(3 + 6 + 8 + 9)`
  `= 12.42…`

`=> D`

Statistics, STD2 S1 2014 HSC 14 MC

Twenty Year 12 students were surveyed. These students were asked how many hours of sport they play per week, to the nearest hour.

The results are shown in the frequency table. 

\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \textit{Hours per week} \rule[-1ex]{0pt}{0pt} & \ \ \ \ \ \textit{Frequency}\ \ \ \ \  \\
\hline
\rule{0pt}{2.5ex} 0-2 \rule[-1ex]{0pt}{0pt} & 5 \\
\hline
\rule{0pt}{2.5ex} 3-5 \rule[-1ex]{0pt}{0pt} & 10 \\
\hline
\rule{0pt}{2.5ex} 6-8 \rule[-1ex]{0pt}{0pt} & 3 \\
\hline
\rule{0pt}{2.5ex}  9-11 \rule[-1ex]{0pt}{0pt} & 2 \\
\hline
\end{array}

 What is the mean number of hours of sport played by the students per week?

  1. 3.3
  2. 4.3
  3. 5.0
  4. 5.3
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Using the class centres}\)

\(\text{Total hours}\) \(=(1\times 5) + (4\times 10) + (7\times 3) + (10\times 2)\)
  \(= 5 + 40 + 21 + 20\)
  \(= 86\)
♦ Mean mark 45%
COMMENT: The mean is calculated using “class centres” in grouped data.
\(\text{Mean hours}\) \(=\dfrac{86}{20} =4.3\)

\(\Rightarrow B\)