| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2017 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Direct cumulative frequency graph reading |
| Difficulty | Easy -1.8 This is a straightforward cumulative frequency graph reading exercise requiring only direct reading of values at specified cumulative frequencies (median at 100th value, quartiles at 50th and 150th, reading frequencies at given x-values, and finding x-value at 94th percentile). No calculations beyond basic subtraction are needed, making it significantly easier than average A-level questions which typically require multi-step problem-solving. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\text{med} = 3.2\) | B1 | Accept \(3.2 \pm 0.05\) |
| \(UQ = 3.65 \leqslant uq \leqslant 3.7\), \(LQ = 2.55 \leqslant lq \leqslant 2.6\) | M1 | \(UQ - LQ\), UQ greater than *their* 'median', LQ less than *their* 'median' |
| \(IQR = 1.05 \leqslant iqr \leqslant 1.15\) | A1 | Correct answer from both LQ and UQ in given ranges |
| Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(134 - 24 = 110\) | B1 | Accept \(108 \leqslant n \leqslant 112\), \(n\) an integer |
| Total: 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(200 - 12 = 188\) less than length \(l\) | M1 | 188 seen, can be implied by answer in range, mark on graph |
| \(l = 4.5\) cm | A1 | Correct answer accept \(4.4 \leqslant l \leqslant 4.5\) |
| Total: 2 |
## Question 2(i):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\text{med} = 3.2$ | B1 | Accept $3.2 \pm 0.05$ |
| $UQ = 3.65 \leqslant uq \leqslant 3.7$, $LQ = 2.55 \leqslant lq \leqslant 2.6$ | M1 | $UQ - LQ$, UQ greater than *their* 'median', LQ less than *their* 'median' |
| $IQR = 1.05 \leqslant iqr \leqslant 1.15$ | A1 | Correct answer from both LQ and UQ in given ranges |
| **Total: 3** | | |
---
## Question 2(ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| $134 - 24 = 110$ | B1 | Accept $108 \leqslant n \leqslant 112$, $n$ an integer |
| **Total: 1** | | |
---
## Question 2(iii):
| Answer | Mark | Guidance |
|--------|------|----------|
| $200 - 12 = 188$ less than length $l$ | M1 | 188 seen, can be implied by answer in range, mark on graph |
| $l = 4.5$ cm | A1 | Correct answer accept $4.4 \leqslant l \leqslant 4.5$ |
| **Total: 2** | | |
---2 Anabel measured the lengths, in centimetres, of 200 caterpillars. Her results are illustrated in the cumulative frequency graph below.\\
\includegraphics[max width=\textwidth, alt={}, center]{184a04ac-4396-4a0f-8fa8-ab11a4b6df39-03_1173_1195_356_466}\\
(i) Estimate the median and the interquartile range of the lengths.\\
(ii) Estimate how many caterpillars had a length of between 2 and 3.5 cm .\\
(iii) 6\% of caterpillars were of length $l$ centimetres or more. Estimate $l$.\\
\hfill \mbox{\textit{CAIE S1 2017 Q2 [6]}}