| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2012 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Find median and quartiles from stem-and-leaf diagram |
| Difficulty | Easy -1.3 This is a straightforward S1 question testing basic understanding of quartiles and stem-and-leaf diagrams. Parts (i)-(iii) involve routine calculations with ordered data (finding Q1, using median to find missing values, finding Q3 range), while (iv)-(v) test simple recall of diagram properties. No problem-solving or novel insight required—purely procedural work with standard definitions. |
| Spec | 2.02f Measures of average and spread |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| 23 | B1 | Allow 22.5. NOT 22 (ie \(3.5^{\text{th}}\) no.). Correct ans is the \(4^{\text{th}}\) or \(3.75^{\text{th}}\) no. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| 0 | B1 | B1 for 30, 30 |
| 0 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| 38 or 40 | B1 for 38 or 39 seen. eg 38, 38.5, 39: B1B0 (ie \(UQ = \frac{3}{4} \times 14 = 10.5^{\text{th}}\) no.) | |
| 39 and 40.75 | B2 | B2 for 38 & 39 seen alone, not in a range. 'Between 39 & 46': B1B0; \(38 \leq\) any letter \(< 40\): B1B0 |
| Mixture eg 38, 40.75 / 3/8 and 3/9 (both) / 8 and 9(both) | B1B0 | SC 42, 42.5 only: B1B0 (ie \(UQ = 11.5^{\text{th}}\) no.). Correct ans are the poss \(11^{\text{th}}\) or \(11.25^{\text{th}}\) nos |
| 40, 40.75: similar scheme as for 38, 39 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Shows all the data / you can see all the values oe / You can see the actual/exact/indiv numbers/values/results / No data is lost oe / Shows the shape of the distribution oe / Can perform calculations of your choice (eg mean) | Any implication of all the data or the actual numbers/values/results or similar. eg Can compare each indiv result; Easier to see the numbers; eg can find frequencies. NOT: Shows the spread/skew/trend; Any comment on skew; You can see the actual frequ's; Easier to compare sets of data; Shows more info or more data; Easier to read off the data. Ignore all other | |
| Shows which group (or class, NOT value) has the highest frequency (or is the mode) oe | B1 | No mks for ans to (v) given in (iv) unless labelled as (v) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Shows the median or it's easier to see the median (or quartiles or IQR) / It can measure the middle 50% easily | B1 | eg Shows mean and quartiles B1; Shows range and median B1. No mks for ans to (v) given in (iv) unless labelled as (v). Ignore all other. NOT: Shows the spread/skew/trend; Can see data in diag form; Shows max or min or range; Easier to compare sets of data; Not affected by outliers; Easy to see outliers; Shows s.d. or shows mean; Can see important data items/measures |
## Question 3:
### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| 23 | B1 | Allow 22.5. NOT 22 (ie $3.5^{\text{th}}$ no.). Correct ans is the $4^{\text{th}}$ or $3.75^{\text{th}}$ no. |
### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| 0 | B1 | B1 for 30, 30 |
| 0 | B1 | |
### Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| 38 or 40 | | B1 for 38 or 39 seen. eg 38, 38.5, 39: B1B0 (ie $UQ = \frac{3}{4} \times 14 = 10.5^{\text{th}}$ no.) |
| 39 and 40.75 | B2 | B2 for 38 & 39 seen alone, not in a range. 'Between 39 & 46': B1B0; $38 \leq$ any letter $< 40$: B1B0 |
| Mixture eg 38, 40.75 / 3/8 and 3/9 (both) / 8 and 9(both) | B1B0 | SC 42, 42.5 only: B1B0 (ie $UQ = 11.5^{\text{th}}$ no.). Correct ans are the poss $11^{\text{th}}$ or $11.25^{\text{th}}$ nos |
| 40, 40.75: similar scheme as for 38, 39 | | |
### Part (iv)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Shows all the data / you can see all the values oe / You can see the actual/exact/indiv numbers/values/results / No data is lost oe / Shows the shape of the distribution oe / Can perform calculations of your choice (eg mean) | | Any implication of all the data or the actual numbers/values/results or similar. eg Can compare each indiv result; Easier to see the numbers; eg can find frequencies. NOT: Shows the spread/skew/trend; Any comment on skew; You can see the actual frequ's; Easier to compare sets of data; Shows more info or more data; Easier to read off the data. Ignore all other |
| Shows which group (or class, NOT value) has the highest frequency (or is the mode) oe | B1 | No mks for ans to (v) given in (iv) unless labelled as (v) |
### Part (v)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Shows the median or it's easier to see the median (or quartiles or IQR) / It can measure the middle 50% easily | B1 | eg Shows mean and quartiles B1; Shows range and median B1. No mks for ans to (v) given in (iv) unless labelled as (v). Ignore all other. NOT: Shows the spread/skew/trend; Can see data in diag form; Shows max or min or range; Easier to compare sets of data; Not affected by outliers; Easy to see outliers; Shows s.d. or shows mean; Can see important data items/measures |
---3 The test marks of 14 students are displayed in a stem-and-leaf diagram, as shown below.\\
\includegraphics[max width=\textwidth, alt={}, center]{e23cb28b-49e5-436a-942d-e6320029c634-2_234_261_1425_482}
Key: 1 | 6 means 16 marks\\
(i) Find the lower quartile.\\
(ii) Given that the median is 32 , find the values of $w$ and $x$.\\
(iii) Find the possible values of the upper quartile.\\
(iv) State one advantage of a stem-and-leaf diagram over a box-and-whisker plot.\\
(v) State one advantage of a box-and-whisker plot over a stem-and-leaf diagram.
\hfill \mbox{\textit{OCR S1 2012 Q3 [7]}}