| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2017 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from grouped frequency table |
| Difficulty | Easy -1.2 This is a standard S1 grouped frequency question requiring routine application of formulas for median (with linear interpolation), mean, and standard deviation from grouped data. All necessary values are provided including Σfx², and the methods are textbook procedures with no problem-solving or insight required. Significantly easier than average A-level maths questions. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Weight of carrot | Frequency (f) | Weight midpoint \(( \boldsymbol { x }\) grams \()\) |
| \(45 - 54\) | 5 | 49.5 |
| \(55 - 59\) | 10 | 57 |
| \(60 - 64\) | 22 | 62 |
| \(65 - 74\) | 13 | 69.5 |
\begin{enumerate}
\item Nina weighed a random sample of 50 carrots from her shop and recorded the weight, in grams to the nearest gram, for each carrot. The results are summarised below.
\end{enumerate}
\begin{center}
\begin{tabular}{ | c | c | c | }
\hline
Weight of carrot & Frequency (f) & Weight midpoint $( \boldsymbol { x }$ grams $)$ \\
\hline
$45 - 54$ & 5 & 49.5 \\
\hline
$55 - 59$ & 10 & 57 \\
\hline
$60 - 64$ & 22 & 62 \\
\hline
$65 - 74$ & 13 & 69.5 \\
\hline
\end{tabular}
\end{center}
$$\text { (You may use } \sum \mathrm { f } x ^ { 2 } = 192102.5 \text { ) }$$
(a) Use linear interpolation to estimate the median weight of these carrots.\\
(b) Find an estimate for the mean weight of these carrots.\\
(c) Find an estimate for the standard deviation of the weights of these carrots.
A carrot is selected at random from Nina's shop.\\
(d) Estimate the probability that the weight of this carrot is more than 70 grams.
\begin{center}
\end{center}
\hfill \mbox{\textit{Edexcel S1 2017 Q1 [8]}}