| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2012 |
| Session | June |
| Marks | 9 |
| 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 given data, finding median/IQR by ordering values, and calculating mean/standard deviation using a calculator. All are routine procedures with no problem-solving or conceptual challenge beyond careful arithmetic. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Flat screen : | 0.85 | 0.94 | 0.91 | 0.96 | 1.04 | 0.89 | 1.07 | 0.92 | 0.76 |
| Conventional : | 0.69 | 0.65 | 0.85 | 0.77 | 0.74 | 0.67 | 0.71 | 0.86 | 0.75 |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Flat screen | conventional | |
| 6 | 5 7 9 | |
| 6 | 7 | 1 4 5 7 |
| 7 | 8 | 5 6 |
| 6 4 2 1 | 9 | |
| 7 4 | 10 | |
| key: 5 | 8 | 4 means 0.85 m for flat screen and 0.84 m for conventional |
| (ii) Conventional median = 0.74 | B1 | Correct median |
| conv IQ range = 0.81 − 0.68 = 0.13 | M1 | Their UQ − their LQ |
| A1 [3] | Correct answer | |
| (iii) mean = 0.927 | B1 | Need 3 s.f. (Accept 0.0878 to 0.0889) |
| sd = 0.0882 | B1 [2] |
**(i)** Flat screen | conventional | | B1 | Correct stem must be integers
| 6 | 5 7 9 | |
| 6 | 7 | 1 4 5 7 | B1 | Correct flat screen leaves
| 7 | 8 | 5 6 | |
| 6 4 2 1 | 9 | | B1 | Correct conventional screen leaves
| 7 4 | 10 | | |
| | | |
key: 5 | 8 | 4 means 0.85 m for flat screen and 0.84 m for conventional | B1 [4] | Key must have units and TV type
**(ii)** Conventional median = 0.74 | B1 | Correct median
conv IQ range = 0.81 − 0.68 = 0.13 | M1 | Their UQ − their LQ
| A1 [3] | Correct answer
**(iii)** mean = 0.927 | B1 | Need 3 s.f. (Accept 0.0878 to 0.0889)
sd = 0.0882 | B1 [2]5 The lengths of the diagonals in metres of the 9 most popular flat screen TVs and the 9 most popular conventional TVs are shown below.
\begin{center}
\begin{tabular}{ r l l l l l l l l l }
Flat screen : & 0.85 & 0.94 & 0.91 & 0.96 & 1.04 & 0.89 & 1.07 & 0.92 & 0.76 \\
Conventional : & 0.69 & 0.65 & 0.85 & 0.77 & 0.74 & 0.67 & 0.71 & 0.86 & 0.75 \\
\end{tabular}
\end{center}
(i) Represent this information on a back-to-back stem-and-leaf diagram.\\
(ii) Find the median and the interquartile range of the lengths of the diagonals of the 9 conventional TVs.\\
(iii) Find the mean and standard deviation of the lengths of the diagonals of the 9 flat screen TVs.
\hfill \mbox{\textit{CAIE S1 2012 Q5 [9]}}