| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2016 |
| Session | Specimen |
| Marks | 5 |
| Topic | Measures of Location and Spread |
| Type | Identify outliers using IQR rule |
| Difficulty | Easy -1.2 This is a straightforward application of standard statistical procedures: ordering data, finding quartiles using a standard method, and applying the IQR × 1.5 outlier rule. It requires only routine recall and calculation with no problem-solving insight, making it easier than average. |
| Spec | 2.02f Measures of average and spread |
| Car | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O |
| Mpg | 57 | 40 | 34 | 33 | 11 | 17 | 30 | 27 | 31 | 20 | 35 | 24 | 26 | 23 | 32 |
**Question 3**
(i) Median $= 30$ mpg [B1]
Quartiles $= 34$ mpg and $23$ mpg [B1]
(ii) $IQR = 11$ mpg [M1]
Outliers have mpg $< 6.5$ or $> 50.5$ [A1]
Car A [B1]
**Total: 5 marks**3 The table shows fuel economy figures in miles per gallon (mpg) for some new cars.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | c | c | c | c | c | c | c | }
\hline
Car & A & B & C & D & E & F & G & H & I & J & K & L & M & N & O \\
\hline
Mpg & 57 & 40 & 34 & 33 & 11 & 17 & 30 & 27 & 31 & 20 & 35 & 24 & 26 & 23 & 32 \\
\hline
\end{tabular}
\end{center}
(i) Find the median and quartiles for the mpg of these fifteen cars.\\
(ii) Use the values in part (i) to identify any cars for which the mpg is an outlier.
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2016 Q3 [5]}}