| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Use linear interpolation for median or quartiles |
| Difficulty | Moderate -0.3 This is a standard S1 grouped data question requiring routine application of linear interpolation for the median, calculation of mean and standard deviation from a frequency table, and interpretation of a given skewness formula. All techniques are textbook procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Foot length, \(l\), (cm) | Number of children |
| \(10 \leqslant l < 12\) | 5 |
| \(12 \leqslant l < 17\) | 53 |
| \(17 \leqslant l < 19\) | 29 |
| \(19 \leqslant l < 21\) | 15 |
| \(21 \leqslant l < 23\) | 11 |
| \(23 \leqslant l < 25\) | 7 |
4. A researcher measured the foot lengths of a random sample of 120 ten-year-old children. The lengths are summarised in the table below.
\begin{center}
\begin{tabular}{|l|l|}
\hline
Foot length, $l$, (cm) & Number of children \\
\hline
$10 \leqslant l < 12$ & 5 \\
\hline
$12 \leqslant l < 17$ & 53 \\
\hline
$17 \leqslant l < 19$ & 29 \\
\hline
$19 \leqslant l < 21$ & 15 \\
\hline
$21 \leqslant l < 23$ & 11 \\
\hline
$23 \leqslant l < 25$ & 7 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Use interpolation to estimate the median of this distribution.
\item Calculate estimates for the mean and the standard deviation of these data.
One measure of skewness is given by
$$\text { Coefficient of skewness } = \frac { 3 ( \text { mean } - \text { median } ) } { \text { standard deviation } }$$
\item Evaluate this coefficient and comment on the skewness of these data.
Greg suggests that a normal distribution is a suitable model for the foot lengths of ten-year-old children.
\item Using the value found in part (c), comment on Greg's suggestion, giving a reason for your answer.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2009 Q4 [13]}}