| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from discrete frequency table |
| Difficulty | Moderate -0.3 This is a straightforward S1 statistics question requiring standard calculations from a frequency table (median, IQR, mean, standard deviation) and basic conceptual understanding about how adding zero values affects these measures. All techniques are routine textbook exercises with no novel problem-solving required, though the multi-part nature and conceptual reasoning in part (b) elevate it slightly above pure mechanical calculation. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.04h Select appropriate distribution |
| Number of children \(( \boldsymbol { x } )\) | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Number of households \(( \boldsymbol { f } )\) | 14 | 35 | 25 | 13 | 9 | 2 | 1 |
5 A survey of all the households on an estate is undertaken to provide information on the number of children per household.
The results, for the 99 households with children, are shown in the table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | }
\hline
Number of children $( \boldsymbol { x } )$ & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
Number of households $( \boldsymbol { f } )$ & 14 & 35 & 25 & 13 & 9 & 2 & 1 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item For these 99 households, calculate values for:
\begin{enumerate}[label=(\roman*)]
\item the median and the interquartile range;
\item the mean and the standard deviation.
\end{enumerate}\item In fact, 163 households were surveyed, of which 64 contained no children.
\begin{enumerate}[label=(\roman*)]
\item For all 163 households, calculate the value for the mean number of children per household.
\item State whether the value for the standard deviation, when calculated for all 163 households, will be smaller than, the same as, or greater than that calculated in part (a)(ii).
\item It is claimed that, for all 163 households on the estate, the number of children per household may be modelled approximately by a normal distribution.
Comment, with justification, on this claim. Your comment should refer to a fact other than the discrete nature of the data.\\
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{adf1c0d2-b0a6-4a2f-baf2-cfb45d771315-11_2484_1709_223_153}
\end{center}
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA S1 2009 Q5 [11]}}