S1 June 2014 Q2
2. The mark, \(x\), scored by each student who sat a statistics examination is coded using
\[y = 1.4x - 20\]The coded marks have mean 60.8 and standard deviation 6.60
Find the mean and the standard deviation of \(x\). (4)
| Scheme | Marks |
|---|---|
| mean \(= \dfrac{60.8 + 20}{1.4}\) or \(60.8 = 1.4x - 20\) (o.e.) | M1 |
| \(= 57.7142\ldots\) awrt 57.7 | A1 |
| standard deviation \(= \dfrac{6.60}{1.4}\) or \(6.60 = 1.4x\) | M1 |
| \(= 4.7142\ldots\) awrt 4.71 | A1 |
| (4) | |
| (4 marks) |
Notes
1st M1 sub. 60.8 for \(y\) into a correct equation. Allow use of \(x\) or any other letter or expression for mean
1st A1 for awrt 57.7 or \(\dfrac{404}{7}\) (o.e.). Correct answer only is 2/2
2nd M1 sub. 6.60 or 6.6 for \(y\) and ignoring the 20. Allow use of \(x\) or any other letter or expression for st. dev. \(6.60^2 = 1.4^2x^2\) is M0 until we see them take a square root.
2nd A1 for awrt 4.71 or \(\dfrac{33}{7}\) (o.e.). Correct answer only is 2/2