| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Estimate mean and standard deviation from frequency table |
| Difficulty | Moderate -0.8 This is a straightforward S1 question requiring standard procedures: finding median/percentile from grouped data using interpolation, and calculating histogram bar dimensions using frequency density. All techniques are routine textbook exercises with no problem-solving or novel insight required, making it easier than average but not trivial due to the multi-step nature. |
| Spec | 2.02b Histogram: area represents frequency2.02f Measures of average and spread |
| Weight (g) | \(14 - 19\) | \(20 - 21\) | \(22 - 23\) | \(24 - 25\) | \(26 - 29\) | \(30 - 35\) |
| Frequency | 3 | 6 | 15 | 20 | 9 | 2 |
| Answer | Marks |
|---|---|
| (a)(i) median = \(28^{th} = 23.5 + (\frac{4}{30} \times 2) = 23.9\) g | M1 A1 |
| (a)(ii) \(33^{rd}\) percentile = \(\frac{33}{100} \times (55+1)th = 18.48^{th}\) value = \(21.5 + (\frac{9.48}{13} \times 2) = 22.8\) g | M1 A1 |
| (b) 24 - 25: class width \(2 \to 1\) cm \(\therefore\) class width \(1 \to 0.5\) cm; freq. den. = \(\frac{50}{10} = 10 \to 20\) cm \(\therefore\) freq. den. \(1 \to 2\) cm | M1 M1 |
| (b)(i) 20 - 21: class width 2 \(\therefore\) width 1 cm; freq. den. = \(\frac{6}{2} = 3 \therefore\) height 6 cm | A1 A1 |
| (b)(ii) 26 - 29: class width 4 \(\therefore\) width 2 cm; freq. den. = \(\frac{9}{4} = 2.25 \therefore\) height 4.5 cm | A1 A1 |
| (11) |
**(a)(i)** median = $28^{th} = 23.5 + (\frac{4}{30} \times 2) = 23.9$ g | M1 A1 |
**(a)(ii)** $33^{rd}$ percentile = $\frac{33}{100} \times (55+1)th = 18.48^{th}$ value = $21.5 + (\frac{9.48}{13} \times 2) = 22.8$ g | M1 A1 |
**(b)** 24 - 25: class width $2 \to 1$ cm $\therefore$ class width $1 \to 0.5$ cm; freq. den. = $\frac{50}{10} = 10 \to 20$ cm $\therefore$ freq. den. $1 \to 2$ cm | M1 M1 |
**(b)(i)** 20 - 21: class width 2 $\therefore$ width 1 cm; freq. den. = $\frac{6}{2} = 3 \therefore$ height 6 cm | A1 A1 |
**(b)(ii)** 26 - 29: class width 4 $\therefore$ width 2 cm; freq. den. = $\frac{9}{4} = 2.25 \therefore$ height 4.5 cm | A1 A1 |
| | | (11) |
---\begin{enumerate}
\item A net was used to catch swallows so that they could be ringed and examined. The weights of 55 adult birds were recorded and the results are summarised in the table below.
\end{enumerate}
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | }
\hline
Weight (g) & $14 - 19$ & $20 - 21$ & $22 - 23$ & $24 - 25$ & $26 - 29$ & $30 - 35$ \\
\hline
Frequency & 3 & 6 & 15 & 20 & 9 & 2 \\
\hline
\end{tabular}
\end{center}
(a) For these data calculate estimates of\\
(i) the median,\\
(ii) the $33 ^ { \text {rd } }$ percentile.
These data are represented by a histogram and the bar representing the 24-25 group is 1 cm wide and 20 cm high.\\
(b) Calculate the dimensions of the bars representing the groups\\
(i) 20-21\\
(ii) 26-29\\
\hfill \mbox{\textit{Edexcel S1 Q1 [11]}}