| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2017 |
| Session | March |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Find median and quartiles from stem-and-leaf diagram |
| Difficulty | Easy -1.8 This is a straightforward data handling question requiring only basic counting skills to find the median and quartiles from an already-organized stem-and-leaf diagram (n=59, so median is 30th value, quartiles are 15th and 45th values), then plotting these five-number summary values on a provided grid. Part (ii) requires recognizing a symmetric distribution pattern, which is direct observation. No calculations beyond counting positions are needed. |
| Spec | 2.02b Histogram: area represents frequency5.01b Selection/arrangement: probability problems |
| 747 | 3 | \(( 1 )\) | |||||||||||||||
| 748 | 1 | 2 | 5 | 7 | 7 | 9 | \(( 6 )\) | ||||||||||
| 749 | 0 | 2 | 2 | 2 | 3 | 5 | 5 | 5 | 6 | 7 | 8 | 9 | \(( 12 )\) | ||||
| 750 | 1 | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 5 | 6 | 7 | 7 | 8 | 8 | 9 | \(( 15 )\) | |
| 751 | 0 | 0 | 2 | 3 | 3 | 4 | 4 | 4 | 5 | 5 | 7 | 7 | 9 | \(( 13 )\) | |||
| 752 | 0 | 0 | 0 | 1 | 1 | 2 | 2 | 3 | 4 | 4 | 4 | \(( 11 )\) | |||||
| 753 | 2 | \(( 1 )\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(LQ = 0.7495\), \(Med = 0.7507\), \(UQ = 0.7517\) | M1 | Attempt to find all 3 quartiles can be implied; Condone LQ=0.7496, Med=0.7506, UQ=0.7515 |
| Correct median line in box | B1 | Correct median line in box using their scale |
| Correct quartiles in box | A1 | |
| Correct end whiskers (not dots or boxes), lines not through box | B1 | |
| Correct uniform scale from at least 0.7473 to 0.7532, and label (wt) kg | B1 | Label can be seen in title or scale |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Normal | B1 | |
| Symmetrical / peaks in middle or tails off quickly | B1 | Need symm + another reason |
# Question 4(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $LQ = 0.7495$, $Med = 0.7507$, $UQ = 0.7517$ | M1 | Attempt to find all 3 quartiles can be implied; Condone LQ=0.7496, Med=0.7506, UQ=0.7515 |
| Correct median line in box | B1 | Correct median line in box using their scale |
| Correct quartiles in box | A1 | |
| Correct end whiskers (not dots or boxes), lines not through box | B1 | |
| Correct uniform scale from at least 0.7473 to 0.7532, and label (wt) kg | B1 | Label can be seen in title or scale |
---
# Question 4(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Normal | B1 | |
| Symmetrical / peaks in middle or tails off quickly | B1 | Need symm + another reason |
---4 The weights in kilograms of packets of cereal were noted correct to 4 significant figures. The following stem-and-leaf diagram shows the data.
\begin{center}
\begin{tabular}{ l | l l l l l l l l l l l l l l l l l }
747 & 3 & & & & & & & & & & & & & & & & $( 1 )$ \\
748 & 1 & 2 & 5 & 7 & 7 & 9 & & & & & & & & & & & $( 6 )$ \\
749 & 0 & 2 & 2 & 2 & 3 & 5 & 5 & 5 & 6 & 7 & 8 & 9 & & & & $( 12 )$ & \\
750 & 1 & 1 & 2 & 2 & 2 & 3 & 4 & 4 & 5 & 6 & 7 & 7 & 8 & 8 & 9 & $( 15 )$ & \\
751 & 0 & 0 & 2 & 3 & 3 & 4 & 4 & 4 & 5 & 5 & 7 & 7 & 9 & & & $( 13 )$ & \\
752 & 0 & 0 & 0 & 1 & 1 & 2 & 2 & 3 & 4 & 4 & 4 & & & & & $( 11 )$ & \\
753 & 2 & & & & & & & & & & & & & & & $( 1 )$ & \\
\end{tabular}
\end{center}
Key: 748 | 5 represents 0.7485 kg .\\
(i) On the grid, draw a box-and-whisker plot to represent the data.\\
\includegraphics[max width=\textwidth, alt={}, center]{556a1cc2-47ef-4ef7-a8f6-42850c303531-05_814_1604_1336_299}\\
(ii) Name a distribution that might be a suitable model for the weights of this type of cereal packet. Justify your answer.\\
\hfill \mbox{\textit{CAIE S1 2017 Q4 [7]}}