| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2013 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Construct stem-and-leaf then find median and quartiles |
| Difficulty | Easy -1.8 This is a straightforward data handling question requiring only basic statistical skills: constructing a stem-and-leaf diagram (routine procedure), calculating mean and median from given data (direct application of formulas), and simple reasoning about how correcting one value affects the median. All parts are standard textbook exercises with no problem-solving or conceptual depth required. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Answer | Marks | Guidance |
|---|---|---|
| - Stem: 2 | 0, 3 | 2, 4 |
| - 2 | 4 means 24 or similar |
### (i)
**Answer:**
- Stem: 2|0, 3|2, 4|0, 5|3, 6|2 with leaves 4, 3, 5, 5, 5, 7, 7, 9, 9 arranged as shown
- 2|4 means 24 or similar
**Marks:** B1, B1, B1[3]
**Guidance:**
- B1 for stem correct AND (3 branches correct OR 5 branches correct with nos but incorrectly ordered)
- Allow incorrect alignment
- Allow space instead of line
- Allow left-facing diagram
- B1 for all correct: If all digits in correct rows and orders, award this mark unless: 4th row is not the longest OR eg a 3rd digit in one row clearly aligned with a 4th digit in another
### (ii)
**Answer:** $47.6$ (3 sf) or $\frac{857}{18}$ or $47\frac{11}{18}$ (cm) or $51$ (cm)
**Marks:** B1, B1, B1ft[2]
**Guidance:**
- B1 cao (correct answer only)
- B1ft (follow through with wrong diagram): eg $857 \div 18 = 41.6$, B0 but $\frac{857}{18} = 41.6$ ISW B1
### (iii)
**Answer:**
- $49$ (or $9^{\text{th}}$ no.) becomes $51$
- or $53$ (or $10^{\text{th}}$ no.) becomes $55$
**Marks:** B1, B1[2]
**Guidance:**
- No marks for identifying 49 & 53 alone or 51 & 55 alone
- NB NO ft from wrong diagram
- NOT eg '51 or higher'
- Allow embedded answer, eg 53 identified as incorrect and state$(55+49)÷2=52$ scores 2nd B1
---The lengths, in centimetres, of 18 snakes are given below.
24 62 20 65 27 67 69 32 40 53 55 47 33 45 55 56 49 58
\begin{enumerate}[label=(\roman*)]
\item Draw an ordered stem-and-leaf diagram for the data. [3]
\item Find the mean and median of the lengths of the snakes. [2]
\item It was found that one of the lengths had been measured incorrectly. After this length was corrected, the median increased by 1 cm. Give two possibilities for the incorrect length and give a corrected value in each case. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR S1 2013 Q1 [7]}}