| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw histogram then find median/quartiles from cumulative frequency |
| Difficulty | Moderate -0.3 This is a standard S1 histogram and summary statistics question requiring routine application of frequency density calculation, linear interpolation for median/quartiles, and basic skewness interpretation. While multi-part with several steps, all techniques are textbook procedures with no problem-solving insight required, making it slightly easier than average. |
| Spec | 2.02b Histogram: area represents frequency2.02f Measures of average and spread |
| Number of people | Number of showings |
| 1-40 | 36 |
| 41-60 | 20 |
| 61-80 | 33 |
| 81-100 | 24 |
| 101-150 | 36 |
| 151-200 | 39 |
| 201-300 | 52 |
| Answer | Marks | Guidance |
|---|---|---|
| freq. dens. = 0.9, 1, 1.65, 1.2, 0.72, 0.78, 0.52 | M1 A1 | |
| [Histogram shown] | B2 | |
| cum. freqs: 36, 56, 89, 113, 149, 188, 240 | M1 | |
| \(Q_1 = 60^{\text{th}} = 60.5 + 20(\frac{3}{4}) = 62.9\) [60.25 → 63.1] | M2 A3 | |
| \(Q_2 = 120^{\text{th}} = 100.5 + 50(\frac{7}{36}) = 110.2\) [120.5th → 110.9] | ||
| \(Q_3 = 180^{\text{th}} = 150.5 + 50(\frac{31}{39}) = 190.2\) [180.75th → 191.2] | ||
| \(Q_3 - Q_2 = 80.0, Q_2 - Q_1 = 47.3; Q_3 - Q_2 > Q_2 - Q_1 \therefore +\)ve skew | M2 A1 | (13) |
freq. dens. = 0.9, 1, 1.65, 1.2, 0.72, 0.78, 0.52 | M1 A1 |
[Histogram shown] | B2 |
cum. freqs: 36, 56, 89, 113, 149, 188, 240 | M1 |
$Q_1 = 60^{\text{th}} = 60.5 + 20(\frac{3}{4}) = 62.9$ [60.25 → 63.1] | M2 A3 |
$Q_2 = 120^{\text{th}} = 100.5 + 50(\frac{7}{36}) = 110.2$ [120.5th → 110.9] |
$Q_3 = 180^{\text{th}} = 150.5 + 50(\frac{31}{39}) = 190.2$ [180.75th → 191.2] |
$Q_3 - Q_2 = 80.0, Q_2 - Q_1 = 47.3; Q_3 - Q_2 > Q_2 - Q_1 \therefore +$ve skew | M2 A1 | (13)6. A cinema recorded the number of people at each showing of each film during a one-week period. The results are summarised in the table below.
\begin{center}
\begin{tabular}{|l|l|}
\hline
Number of people & Number of showings \\
\hline
1-40 & 36 \\
\hline
41-60 & 20 \\
\hline
61-80 & 33 \\
\hline
81-100 & 24 \\
\hline
101-150 & 36 \\
\hline
151-200 & 39 \\
\hline
201-300 & 52 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw a histogram on graph paper to illustrate these data.
\item Calculate estimates of the median and quartiles of these data.
\item Use your answers to part (b) to show that the data is positively skewed.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q6 [13]}}