| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Direct cumulative frequency graph reading |
| Difficulty | Easy -1.3 This is a straightforward cumulative frequency question requiring only direct reading from a table and basic calculations. Parts (i) and (iii) are simple lookups, part (ii) involves standard quartile calculations with given cumulative frequencies, and part (iv) is routine histogram drawing. No problem-solving or conceptual insight required—purely procedural application of basic statistics techniques. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02b Histogram: area represents frequency2.02f Measures of average and spread |
| Weight (grams) | \(< 20\) | \(< 30\) | \(< 40\) | \(< 45\) | \(< 50\) | \(< 60\) | \(< 70\) |
| Cumulative frequency | 0 | 20 | 50 | 100 | 160 | 210 | 220 |
| Answer | Marks | Guidance |
|---|---|---|
| (i) 45 − 50 g | B1 | [1] |
| (ii) LQ in 40 − 45, UQ in 50 − 60. Smallest IQ range could be 5, Largest IQ range could be 20 | M1, A1 | [2] Considering groups containing LQ and UQ (can be implied); Correct answer |
| (iii) 50 | B1 | [1] |
| (iv) freqs 0, 20, 30, 50, 60, 50, 10; fd 0, 2, 3, 10, 12, 5, 1 | M1 | Attempt at frequencies and fd |
| [Histogram with correct labels and scales] | B1 | Correct labels and scales with a histogram-type shape |
| [Histogram with bars of correct width starting at 20] | B1 | Correct bar widths starting at 20 |
| [Histogram with correct heights of bars] | A1 | [4] Correct heights of bars |
**(i)** 45 − 50 g | B1 | [1]
**(ii)** LQ in 40 − 45, UQ in 50 − 60. Smallest IQ range could be 5, Largest IQ range could be 20 | M1, A1 | [2] Considering groups containing LQ and UQ (can be implied); Correct answer
**(iii)** 50 | B1 | [1]
**(iv)** freqs 0, 20, 30, 50, 60, 50, 10; fd 0, 2, 3, 10, 12, 5, 1 | M1 | Attempt at frequencies and fd
[Histogram with correct labels and scales] | B1 | Correct labels and scales with a histogram-type shape
[Histogram with bars of correct width starting at 20] | B1 | Correct bar widths starting at 20
[Histogram with correct heights of bars] | A1 | [4] Correct heights of bars4 The weights of 220 sausages are summarised in the following table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | }
\hline
Weight (grams) & $< 20$ & $< 30$ & $< 40$ & $< 45$ & $< 50$ & $< 60$ & $< 70$ \\
\hline
Cumulative frequency & 0 & 20 & 50 & 100 & 160 & 210 & 220 \\
\hline
\end{tabular}
\end{center}
(i) State which interval the median weight lies in.\\
(ii) Find the smallest possible value and the largest possible value for the interquartile range.\\
(iii) State how many sausages weighed between 50 g and 60 g .\\
(iv) On graph paper, draw a histogram to represent the weights of the sausages.
\hfill \mbox{\textit{CAIE S1 2011 Q4 [8]}}