| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2018 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Histogram from discrete rounded data |
| Difficulty | Moderate -0.8 This is a straightforward S1 question requiring basic statistical skills: locating the lower quartile (n/4 = 12.5, so 13th value falls in the 15-19 class) and drawing a histogram with unequal class widths requiring frequency density calculations. Both are standard textbook exercises with no problem-solving or conceptual challenges beyond routine application of learned procedures. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02b Histogram: area represents frequency2.02f Measures of average and spread |
| Mass (kg) | \(10 - 14\) | \(15 - 19\) | \(20 - 24\) | \(25 - 34\) | \(35 - 59\) |
| Frequency | 6 | 12 | 14 | 10 | 8 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(15\)–\(19\) (kg) cao | B1 | kg not necessary; condone \(14.5\) – \(19.5\) |
| Total: 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(fd = 1.2,\ 2.4, \ 2.8, \ 1, \ 0.32\) | M1 | Attempt at \(fd\) \([f/(\text{attempt at } cw)]\) or scaled freq (may be implied by 4 correct) |
| Correct heights on diagram with linear vertical scale from \((x, 0)\) | A1 | Correct heights seen on diagram with linear vertical scale from \((x, 0)\) |
| Correct bar widths \((1:1:1:2:5)\) visually no gaps with linear horizontal scale from \((9.5, y)\) and first bar starting at \((9.5, y)\) | B1 | Correct bar widths \((1:1:1:2:5)\) visually no gaps with linear horizontal scale from \((9.5, y)\) and first bar starting at \((9.5, y)\) |
| Histogram, using attempted \(fd\)s, with labels (mass, kg and \(fd\) seen) and at least 3 linearly spaced values on each axis. Horizontal axis must range from at least \(9.5\) to \(59.5\). If horizontal axis clearly starts from zero, either a break in the scale must be indicated or the scale must be linear from zero. | B1 |
## Question 1:
### Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $15$–$19$ (kg) cao | **B1** | kg not necessary; condone $14.5$ – $19.5$ |
| **Total: 1** | | |
---
### Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $fd = 1.2,\ 2.4, \ 2.8, \ 1, \ 0.32$ | **M1** | Attempt at $fd$ $[f/(\text{attempt at } cw)]$ or scaled freq (may be implied by 4 correct) |
| Correct heights on diagram with linear vertical scale from $(x, 0)$ | **A1** | Correct heights seen on diagram with linear vertical scale from $(x, 0)$ |
| Correct bar widths $(1:1:1:2:5)$ visually no gaps with linear horizontal scale from $(9.5, y)$ and first bar starting at $(9.5, y)$ | **B1** | Correct bar widths $(1:1:1:2:5)$ visually no gaps with linear horizontal scale from $(9.5, y)$ and first bar starting at $(9.5, y)$ |
| Histogram, using attempted $fd$s, with labels (mass, kg and $fd$ seen) and at least 3 linearly spaced values on each axis. Horizontal axis must range from at least $9.5$ to $59.5$. If horizontal axis clearly starts from zero, either a break in the scale must be indicated or the scale must be linear from zero. | **B1** | |1 The masses in kilograms of 50 children having a medical check-up were recorded correct to the nearest kilogram. The results are shown in the table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Mass (kg) & $10 - 14$ & $15 - 19$ & $20 - 24$ & $25 - 34$ & $35 - 59$ \\
\hline
Frequency & 6 & 12 & 14 & 10 & 8 \\
\hline
\end{tabular}
\end{center}
(i) Find which class interval contains the lower quartile.\\
(ii) On the grid, draw a histogram to illustrate the data in the table.\\
\includegraphics[max width=\textwidth, alt={}, center]{dd75fa20-fead-48d6-aff4-c5e733769f9f-02_1397_1397_1187_415}
\hfill \mbox{\textit{CAIE S1 2018 Q1 [5]}}