| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2024 |
| Session | January |
| Marks | 4 |
| Topic | Normal Distribution |
| Type | Estimate from summary statistics |
| Difficulty | Easy -1.8 This is a straightforward calculation question requiring only basic formulas for mean (Σx/n) and variance (Σx²/n - x̄²), followed by simply stating the Normal distribution notation. It involves no problem-solving, conceptual understanding, or interpretation—purely mechanical arithmetic with standard summary statistics formulas that are typically given on formula sheets. |
| Spec | 2.02g Calculate mean and standard deviation2.04e Normal distribution: as model N(mu, sigma^2) |
At the beginning of the academic year, all the pupils in year 12 at a college take part in an assessment. Summary statistics for the marks obtained by the 2021 cohort are given below.
$n = 205$ $\sum x = 23042$ $\sum x^2 = 2591716$
Marks may only be whole numbers, but the Head of Mathematics believes that the distribution of marks may be modelled by a Normal distribution.
\begin{enumerate}[label=(\alph*)]
\item Calculate
\begin{itemize}
\item The mean mark
\item The variance of the marks
\end{itemize}
[2]
\item Use your answers to part (a) to write down a possible Normal model for the distribution of marks. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2024 Q1 [4]}}