Moderate -0.8 This is a straightforward application of the standard deviation formula with given values. Students must substitute into the variance formula for combined datasets, but the algebra is simplified by the symmetric marks (m±4) and the question tells them the answer to verify. It requires careful calculation but no problem-solving insight.
The marks of 24 students in a test had mean \(m\) and standard deviation \(\sqrt{6}\). Two new students took the same test. Their marks were \(m - 4\) and \(m + 4\).
Show that the standard deviation of the marks of all 26 students is 2.60, correct to 3 significant figures. [3]
The marks of 24 students in a test had mean $m$ and standard deviation $\sqrt{6}$. Two new students took the same test. Their marks were $m - 4$ and $m + 4$.
Show that the standard deviation of the marks of all 26 students is 2.60, correct to 3 significant figures. [3]
\hfill \mbox{\textit{OCR H240/02 2018 Q13 [3]}}