| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Compare using calculated statistics |
| Difficulty | Moderate -0.8 This is a straightforward S1 question testing basic descriptive statistics (mean, standard deviation, median, IQR) with routine calculations and standard interpretations. Parts (i)-(ii) are mechanical computations, while parts (iii)-(v) test understanding of spread measures at a basic level—recognizing that SD measures overall spread while IQR measures middle 50%, and that lower SD indicates consistency not improvement. No problem-solving or novel insight required, just recall and application of standard concepts. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
### Part i
**Answer:** $\Sigma x ÷ 11$ = 70. $\Sigma x^2$ attempted $\sqrt{\frac{\Sigma x^2}{11} - x̄^2} = \sqrt{(\frac{54210}{11}) - 70^2}$ or $\sqrt{28.18}$ or 5.309 (= 5.31) AG
**Marks:** M1, A1, M1, A1 4
**Guidance:** $\geq 5$ terms, or $\Sigma(x - x̄)^2$ or $\sqrt{\frac{\Sigma(x - x̄)^2}{11}} = \sqrt{\frac{10}{11}}$ or $\sqrt{28.18}$. If $x = \frac{1}{10}$: M1A1M1A0
### Part ii
**Answer:** Attempt arrange in order. med = 67. 74 and 66. IQR = 8
**Marks:** M1, A1, M1, A1 4
**Guidance:** or (72.5 – 76.5) – (65.5 – 66.5) incl. must be from 74 – 66
### Part iii
**Answer:** no (or fewer) extremes this year oe. sd takes account of all values. sd affected by extremes. less spread tho' middle 50% same. less spread tho' 3rd & 9th same or same gap
**Marks:** B1 1
**Guidance:** iii, iv & v: ignore extras. fewer high &/or low scores. highest score(s) less than last year. Not less spread or more consistent. Not range less
### Part iv
**Answer:** sd measures spread or variation or consistency oe
**Marks:** B1 1
**Guidance:** sd less means spread is less oe or marks are closer together oe
### Part v
**Answer:** more consistent, more similar, closer together, nearer to mean. less spread
**Marks:** B1 1
**Guidance:** allow less variance. Not range less. Not highest & lowest closer
---Last year Eleanor played 11 rounds of golf. Her scores were as follows:
79, 71, 80, 67, 67, 74, 66, 65, 71, 66, 64.
\begin{enumerate}[label=(\roman*)]
\item Calculate the mean of these scores and show that the standard deviation is 5.31, correct to 3 significant figures. [4]
\item Find the median and interquartile range of the scores. [4]
\end{enumerate}
This year, Eleanor also played 11 rounds of golf. The standard deviation of her scores was 4.23, correct to 3 significant figures, and the interquartile range was the same as last year.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Give a possible reason why the standard deviation of her scores was lower than last year although her interquartile range was unchanged. [1]
\end{enumerate}
In golf, smaller scores mean a better standard of play than larger scores. Ken suggests that since the standard deviation was smaller this year, Eleanor's overall standard has improved.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{3}
\item Explain why Ken is wrong. [1]
\item State what the smaller standard deviation does show about Eleanor's play. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR S1 2009 Q6 [11]}}