| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate variance/SD from coded sums |
| Difficulty | Standard +0.3 This is a straightforward application of standard formulas for decoding mean and variance from coded data. Students need to recall the linear coding relationships (mean_x = a + b*mean_y, SD_x = |b|*SD_y) and apply them systematically. While it requires multiple steps and careful arithmetic, it involves no problem-solving or conceptual insight beyond routine S1 procedures. The 9 marks reflect the working required rather than conceptual difficulty. |
| Spec | 2.02g Calculate mean and standard deviation2.02h Recognize outliers5.02c Linear coding: effects on mean and variance |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\bar{y} = \frac{-467}{200}\) | B1 | Can be implied |
| \(\therefore \bar{x} = 2.5\bar{y} + 755.0\) | M1 | |
| \(= 2.5\left(\frac{-467}{200}\right) + 755.0\) | A1 | |
| \(= 749.1625\) | A1 | Accept awrt 749 |
| \(S_y = \sqrt{\frac{9179}{200} - \left(\frac{-467}{200}\right)^2}\) | M1 A1 | |
| \(= 6.35946\) | A1 | |
| \(\therefore S_x = 2.5 \times 6.35946\) | M1 | |
| \(= 15.89865\) | A1 (9) | Accept awrt 15.9 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Standard deviation \(< \frac{2}{3}\) (interquartile range) | B1 | |
| Suggest using standard deviation since it shows less variation in the lifetimes | B1 (2) | (11) |
## Question 3:
### Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\bar{y} = \frac{-467}{200}$ | B1 | Can be implied |
| $\therefore \bar{x} = 2.5\bar{y} + 755.0$ | M1 | |
| $= 2.5\left(\frac{-467}{200}\right) + 755.0$ | A1 | |
| $= 749.1625$ | A1 | Accept awrt 749 |
| $S_y = \sqrt{\frac{9179}{200} - \left(\frac{-467}{200}\right)^2}$ | M1 A1 | |
| $= 6.35946$ | A1 | |
| $\therefore S_x = 2.5 \times 6.35946$ | M1 | |
| $= 15.89865$ | A1 (9) | Accept awrt 15.9 |
### Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Standard deviation $< \frac{2}{3}$ (interquartile range) | B1 | |
| Suggest using standard deviation since it shows less variation in the lifetimes | B1 (2) | **(11)** |
---3. Data relating to the lifetimes (to the nearest hour) of a random sample of 200 light bulbs from the production line of a manufacturer were summarised in a group frequency table. The mid-point of each group in the table was represented by $x$ and the corresponding frequency for that group by $f$. The data were then coded using $y = \frac { ( x - 755.0 ) } { 2.5 }$ and summarised as follows:
$$\Sigma f y = - 467 , \Sigma f y ^ { 2 } = 9179 .$$
\begin{enumerate}[label=(\alph*)]
\item Calculate estimates of the mean and the standard deviation of the lifetimes of this sample of bulbs.\\
(9 marks)\\
An estimate of the interquartile range for these data was 27.7 hours.
\item Explain, giving a reason, whether you would recommend the manufacturer to use the interquartile range or the standard deviation to represent the spread of lifetimes of the bulbs from this production line.\\
(2 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q3 [11]}}