The marks below were recorded by Ms Smith for her students in a recent statistics quiz. The highest possible score was 5.
\(3,\ 1,\ 5,\ 2,\ 1,\ 3,\ 4,\ 1,\ 4,\ 2,\ 4,\ 5,\ 3,\ 4,\ 2,\ 4,\ 3,\ 0,\ 5,\ 1,\ 4\)
- Summarise the data using the table below. (1 mark)
\begin{array} {|l|c|c|c|c||}
\hline
\rule{0pt}{2.5ex} \textbf{Score} \rule[-1ex]{0pt}{0pt} & \ 0\ & \ 1\ & \ 2\ & \ 3\ & \ 4\ & \ 5\ \\
\hline
\rule{0pt}{2.5ex} \textbf{Number of Students} \rule[-1ex]{0pt}{0pt} & &&&&& \\
\hline
\end{array}--- 0 WORK AREA LINES (style=lined) ---
- Represent this data as a column graph using the grid below. (2 marks)
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- How many students sat for the quiz? (1 mark)
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- If the pass mark was 60%, how many students passed the quiz? ( 1 mark)
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- What was the average score achieved in the quiz? Give your answer correct to one decimal place. (1 mark)
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a.
\begin{array} {|l|c|c|c|c||}
\hline
\rule{0pt}{2.5ex} \textbf{Score} \rule[-1ex]{0pt}{0pt} & 0&1&2&3&4&5 \\
\hline
\rule{0pt}{2.5ex} \textbf{Number of Students} \rule[-1ex]{0pt}{0pt} & 1&4&3&4&6&3 \\
\hline
\end{array}
b.
c. \(21\)
d. \(13\)
e. \(2.9\)
a.
\begin{array} {|l|c|c|c|c||}
\hline
\rule{0pt}{2.5ex} \textbf{Score} \rule[-1ex]{0pt}{0pt} & 0&1&2&3&4&5 \\
\hline
\rule{0pt}{2.5ex} \textbf{Number of Students} \rule[-1ex]{0pt}{0pt} & 1&4&3&4&6&3 \\
\hline
\end{array}
b.
c. \(21\)
| d. | \(60\%\ \text{pass mark}\) | \(=5\times \dfrac{60}{100}\) |
| \(=3\) |
\(\therefore\ 4+6+3 = 13\ \text{students passed the quiz}\)
| e. | \(\text{Average score}\) | \(=\dfrac{1\times 0+4\times 1+3\times 2+4\times 3+6\times 4+3\times 5}{21}\) |
| \(=\dfrac{61}{21}\) | ||
| \(=2.904\dots\approx 2.9\ \text{(1 d.p.)}\) |