| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2013 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw box plot from raw data |
| Difficulty | Moderate -0.8 This is a straightforward data representation question requiring calculation of five-number summary from ordered data (n=51 makes quartiles easy to find), drawing a standard box plot, and applying a given outlier definition. All steps are routine recall and calculation with no problem-solving or novel insight required. |
| Spec | 2.02i Select/critique data presentation |
| 253 | 270 | 310 | 354 | 386 | 428 | 433 | 468 | 472 | 477 | 485 | 520 | 520 | 524 | 526 | 531 | 535 |
| 536 | 538 | 541 | 543 | 546 | 548 | 549 | 551 | 554 | 572 | 583 | 590 | 605 | 614 | 638 | 649 | 652 |
| 666 | 670 | 682 | 684 | 690 | 710 | 725 | 726 | 731 | 734 | 745 | 760 | 800 | 854 | 863 | 957 | 986 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Linear scale or 5 values shown and labels in heading, need thousands of dollars | B1 | |
| Correct median | B1 | |
| Correct quartiles | B1 | |
| Correct end points of whiskers not through box | B1 [4] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(1.5 \times 170 = 255\) | M1 | Mult their IQ range by 1.5 |
| Expensive houses above \(690 + 170 \times 1.5 = 945\), i.e. 957 and 986 thousands of dollars | A1 [2] | Correct answers from correct working, need thousands of dollars |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Doesn't show all the data items | B1 [1] | Need to see 'individual items' oe |
## Question 4:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Linear scale or 5 values shown and labels in heading, need thousands of dollars | B1 | |
| Correct median | B1 | |
| Correct quartiles | B1 | |
| Correct end points of whiskers not through box | B1 **[4]** | |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $1.5 \times 170 = 255$ | M1 | Mult their IQ range by 1.5 |
| Expensive houses above $690 + 170 \times 1.5 = 945$, i.e. 957 and 986 thousands of dollars | A1 **[2]** | Correct answers from correct working, need thousands of dollars |
### Part (iii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Doesn't show all the data items | B1 **[1]** | Need to see 'individual items' oe |
---4 The following are the house prices in thousands of dollars, arranged in ascending order, for 51 houses from a certain area.
\begin{center}
\begin{tabular}{ l l l l l l l l l l l l l l l l l }
253 & 270 & 310 & 354 & 386 & 428 & 433 & 468 & 472 & 477 & 485 & 520 & 520 & 524 & 526 & 531 & 535 \\
536 & 538 & 541 & 543 & 546 & 548 & 549 & 551 & 554 & 572 & 583 & 590 & 605 & 614 & 638 & 649 & 652 \\
666 & 670 & 682 & 684 & 690 & 710 & 725 & 726 & 731 & 734 & 745 & 760 & 800 & 854 & 863 & 957 & 986 \\
\end{tabular}
\end{center}
(i) Draw a box-and-whisker plot to represent the data.
An expensive house is defined as a house which has a price that is more than 1.5 times the interquartile range above the upper quartile.\\
(ii) For the above data, give the prices of the expensive houses.\\
(iii) Give one disadvantage of using a box-and-whisker plot rather than a stem-and-leaf diagram to represent this set of data.
\hfill \mbox{\textit{CAIE S1 2013 Q4 [7]}}