| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2017 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw histogram from frequency table |
| Difficulty | Easy -1.2 This is a straightforward histogram drawing question with unequal class widths requiring frequency density calculations, followed by a standard mean estimation from grouped data. Both parts are routine A-level statistics procedures with no problem-solving or conceptual challenges beyond basic recall and calculation. |
| Spec | 2.02b Histogram: area represents frequency2.02g Calculate mean and standard deviation |
| Time \(( t\) seconds \()\) | \(0 \leqslant t < 20\) | \(20 \leqslant t < 40\) | \(40 \leqslant t < 60\) | \(60 \leqslant t < 100\) | \(100 \leqslant t < 140\) |
| Number of people | 320 | 280 | 220 | 220 | 100 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| fd: 16, 14, 11, 505, 2.5 | M1 | Attempt at fd (must be at least 3 freq/cw) – may be implied by graph |
| Correct histogram with appropriate heights | A1 | Correct heights seen on graph i.e. must see a gap for fd \(= 2.5\) etc. |
| B1 | Correct end points of bars and correct widths | |
| B1 | Labels fd, sec. Time can be optional. Linear axes, condone \(0 \leqslant t < 20\) etc. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((10 \times 320 + 30 \times 280 + 50 \times 220 + 80 \times 220 + 120 \times 100) / 1140\) | M1 | Using \(\Sigma fx / n\) with mid-point attempt \(\pm 0.5\), not ends not class widths |
| \(= 45.8\) | A1 |
## Question 4(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| fd: 16, 14, 11, 505, 2.5 | M1 | Attempt at fd (must be at least 3 freq/cw) – may be implied by graph |
| Correct histogram with appropriate heights | A1 | Correct heights seen on graph i.e. must see a gap for fd $= 2.5$ etc. |
| | B1 | Correct end points of bars and correct widths |
| | B1 | Labels fd, sec. Time can be optional. Linear axes, condone $0 \leqslant t < 20$ etc. |
---
## Question 4(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(10 \times 320 + 30 \times 280 + 50 \times 220 + 80 \times 220 + 120 \times 100) / 1140$ | M1 | Using $\Sigma fx / n$ with mid-point attempt $\pm 0.5$, not ends not class widths |
| $= 45.8$ | A1 | |
---4 The times taken, $t$ seconds, by 1140 people to solve a puzzle are summarised in the table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Time $( t$ seconds $)$ & $0 \leqslant t < 20$ & $20 \leqslant t < 40$ & $40 \leqslant t < 60$ & $60 \leqslant t < 100$ & $100 \leqslant t < 140$ \\
\hline
Number of people & 320 & 280 & 220 & 220 & 100 \\
\hline
\end{tabular}
\end{center}
(i) On the grid, draw a histogram to illustrate this information.\\
\includegraphics[max width=\textwidth, alt={}, center]{7652f36c-59b5-4fcd-b17b-d796dc82aec0-05_812_1406_804_411}\\
(ii) Calculate an estimate of the mean of $t$.\\
\hfill \mbox{\textit{CAIE S1 2017 Q4 [6]}}