| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2020 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Construct back-to-back stem-and-leaf from raw data |
| Difficulty | Easy -1.3 This is a straightforward data handling question requiring basic statistical skills: constructing a stem-and-leaf diagram from ordered data, finding median and IQR from 11 values (simple position formulas), and using the mean formula to find a missing value. All parts are routine recall and calculation with no problem-solving or conceptual challenge. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Company \(A\) | 30 | 32 | 35 | 41 | 41 | 42 | 47 | 49 | 52 | 53 | 64 |
| Company \(B\) | 26 | 47 | 30 | 52 | 41 | 38 | 35 | 42 | 49 | 31 | 42 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Correct stem | B1 | KEY: \(1\ |
| Correct A on LHS | B1 | |
| Correct B on same diagram | B1 | |
| Correct key for their diagram, both companies identified and correct units | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Median \(= [\\)]42\,000$ | B1 | |
| \(LQ = [\\)]35\,000\(; \)UQ = [\\(]52\,000\) | B1 | |
| \(IQR = [\\)]17\,000\( | B1 FT | FT if \)49000 \leq UQ \leq 53000 - 32000 \leq LQ \leq 41000$ |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Sum of given 11 numbers is \(433\,000\) | M1 | |
| Sum of 12 numbers including new \(= 38\,500 \times 12 = 462\,000\) | M1 | |
| Difference = new salary \(= [\\)]29\,000$ | A1 |
## Question 6:
### Part (a):
| Answer | Mark | Guidance |
|--------|------|----------|
| Correct stem | B1 | KEY: $1\|4\|2$ means \$41 000 for A and \$42 000 for B |
| Correct A on LHS | B1 | |
| Correct B on same diagram | B1 | |
| Correct key for their diagram, both companies identified and correct units | B1 | |
### Part (b):
| Answer | Mark | Guidance |
|--------|------|----------|
| Median $= [\$]42\,000$ | B1 | |
| $LQ = [\$]35\,000$; $UQ = [\$]52\,000$ | B1 | |
| $IQR = [\$]17\,000$ | B1 FT | FT if $49000 \leq UQ \leq 53000 - 32000 \leq LQ \leq 41000$ |
### Part (c):
| Answer | Mark | Guidance |
|--------|------|----------|
| Sum of given 11 numbers is $433\,000$ | M1 | |
| Sum of 12 numbers including new $= 38\,500 \times 12 = 462\,000$ | M1 | |
| Difference = new salary $= [\$]29\,000$ | A1 | |
---6 The annual salaries, in thousands of dollars, for 11 employees at each of two companies $A$ and $B$ are shown below.
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | l | l | l | l | l | }
\hline
Company $A$ & 30 & 32 & 35 & 41 & 41 & 42 & 47 & 49 & 52 & 53 & 64 \\
\hline
Company $B$ & 26 & 47 & 30 & 52 & 41 & 38 & 35 & 42 & 49 & 31 & 42 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Represent the data by drawing a back-to-back stem-and-leaf diagram with company $A$ on the left-hand side of the diagram.
\item Find the median and the interquartile range of the salaries of the employees in company $A$. [3]\\
A new employee joins company $B$. The mean salary of the 12 employees is now $\$ 38500$.
\item Find the salary of the new employee.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2020 Q6 [10]}}