| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2006 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Standard unbiased estimates calculation |
| Difficulty | Easy -1.2 This is a straightforward question requiring basic recall and routine calculations. Part (i) asks for simple conceptual understanding (increase mean or decrease standard deviation), while part (ii) involves direct application of standard formulas for sample mean and standard deviation with no problem-solving or insight required. The calculations are mechanical with given summations. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Answer | Marks |
|---|---|
| Increase the mean / Decrease the standard deviation | B1 B1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\bar{x} = \frac{11409}{25} = 456.36\) | B1 | |
| \(s^2 = \frac{5206937}{25} - 456.36^2\) or \(\frac{1}{24}\left(5206937 - \frac{11409^2}{25}\right)\) | M1 | |
| \(s = \sqrt{\frac{5206937 - 25 \times 456.36^2}{24}} = \sqrt{\frac{5206937 - 5204534.76}{24}}\) | ||
| \(s \approx 10.02\) | A1 | Accept answers in range 9.9–10.1 |
# Question 4:
**(i)**
Increase the mean / Decrease the standard deviation | B1 B1 |
**(ii)**
$\bar{x} = \frac{11409}{25} = 456.36$ | B1 |
$s^2 = \frac{5206937}{25} - 456.36^2$ or $\frac{1}{24}\left(5206937 - \frac{11409^2}{25}\right)$ | M1 |
$s = \sqrt{\frac{5206937 - 25 \times 456.36^2}{24}} = \sqrt{\frac{5206937 - 5204534.76}{24}}$ | |
$s \approx 10.02$ | A1 | Accept answers in range 9.9–10.1
---4 A company sells sugar in bags which are labelled as containing 450 grams.\\
Although the mean weight of sugar in a bag is more than 450 grams, there is concern that too many bags are underweight. The company can adjust the mean or the standard deviation of the weight of sugar in a bag.\\
(i) State two adjustments the company could make.
The weights, $x$ grams, of a random sample of 25 bags are now recorded.\\
(ii) Given that $\sum x = 11409$ and $\sum x ^ { 2 } = 5206937$, calculate the sample mean and sample standard deviation of these weights.
\hfill \mbox{\textit{OCR MEI S1 2006 Q4 [5]}}