| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2016 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw cumulative frequency graph from frequency table (equal class widths) |
| Difficulty | Easy -1.3 This is a routine statistics question requiring straightforward cumulative frequency calculations and graph plotting. Part (i) involves simple addition to find cumulative frequencies and plotting points; part (ii) requires reading from the graph; part (iii) tests basic understanding of data representation. No problem-solving or novel insight needed—pure procedural recall. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Height of girls (cm) | \(140 < h \leqslant 150\) | \(150 < h \leqslant 160\) | \(160 < h \leqslant 170\) | \(170 < h \leqslant 180\) | \(180 < h \leqslant 190\) |
| Frequency | 12 | 21 | 17 | 10 | 0 |
| Height of boys \(( \mathrm { cm } )\) | \(140 < h \leqslant 150\) | \(150 < h \leqslant 160\) | \(160 < h \leqslant 170\) | \(170 < h \leqslant 180\) | \(180 < h \leqslant 190\) |
| Frequency | 0 | 20 | 23 | 12 | 5 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| cf graph drawn | B1 | Horizontal axis from min of 140 to 190 and vertical axis from 0 to minimum of 60; two CF graphs on same set of axes |
| Labels and correct placement | B1 | Labels: CF; height (ht) in cm; girls; boys in correct places |
| CF graph through \((150,0)\), \((160,20)\), \((170,43)\), \((180,55)\), \((190,60)\) | B1 | |
| CF graph through \((140,0)\), \((150,12)\), \((160,33)\), \((170,50)\), \((180,60)\) [and \((190,60)\)] | B1 [4] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(42\ (\pm 1)\) shorter than 165 | M1 | Line or reading from 165 on their cf graph; oe subtracting from 60 |
| \((18(\pm 1))/60 \times 100 = 30\%\ (\pm 1.7\%)\) | M1, A1 [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Can see which is taller; see which of boys or girls is more spread out | B1 [1] | Any sensible comment in context |
## Question 5:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| cf graph drawn | B1 | Horizontal axis from min of 140 to 190 and vertical axis from 0 to minimum of 60; two CF graphs on same set of axes |
| Labels and correct placement | B1 | Labels: CF; height (ht) in cm; girls; boys in correct places |
| CF graph through $(150,0)$, $(160,20)$, $(170,43)$, $(180,55)$, $(190,60)$ | B1 | |
| CF graph through $(140,0)$, $(150,12)$, $(160,33)$, $(170,50)$, $(180,60)$ [and $(190,60)$] | B1 [4] | |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $42\ (\pm 1)$ shorter than 165 | M1 | Line or reading from 165 on their cf graph; oe subtracting from 60 |
| $(18(\pm 1))/60 \times 100 = 30\%\ (\pm 1.7\%)$ | M1, A1 [3] | |
### Part (iii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Can see which is taller; see which of boys or girls is more spread out | B1 [1] | Any sensible comment in context |
---5 The tables summarise the heights, $h \mathrm {~cm}$, of 60 girls and 60 boys.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Height of girls (cm) & $140 < h \leqslant 150$ & $150 < h \leqslant 160$ & $160 < h \leqslant 170$ & $170 < h \leqslant 180$ & $180 < h \leqslant 190$ \\
\hline
Frequency & 12 & 21 & 17 & 10 & 0 \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Height of boys $( \mathrm { cm } )$ & $140 < h \leqslant 150$ & $150 < h \leqslant 160$ & $160 < h \leqslant 170$ & $170 < h \leqslant 180$ & $180 < h \leqslant 190$ \\
\hline
Frequency & 0 & 20 & 23 & 12 & 5 \\
\hline
\end{tabular}
\end{center}
(i) On graph paper, using the same set of axes, draw two cumulative frequency graphs to illustrate the data.\\
(ii) On a school trip the students have to enter a cave which is 165 cm high. Use your graph to estimate the percentage of the girls who will be unable to stand upright.\\[0pt]
(iii) The students are asked to compare the heights of the girls and the boys. State one advantage of using a pair of box-and-whisker plots instead of the cumulative frequency graphs to do this. [1]
\hfill \mbox{\textit{CAIE S1 2016 Q5 [8]}}