Moderate -0.8 This is a straightforward cumulative frequency graph interpretation question requiring students to read off median and quartiles, calculate IQR, and make simple comparative statements. It's routine statistical description with no calculation complexity or novel insight required—easier than average A-level content.
4 The Mathematics and English A-level marks of 1400 pupils all taking the same examinations are shown in the cumulative frequency graphs below. Both examinations are marked out of 100 .
\includegraphics[max width=\textwidth, alt={}, center]{be6c6525-a20c-42d0-8fef-1cd254baaa76-06_1682_1246_404_445}
Use suitable data from these graphs to compare the central tendency and spread of the marks in Mathematics and English.
Indication of finding medians, such as mark on graph or reference marks to 700 pupils, condone poor terminology such as 'mean'
Median English \(= 55\)
A1
Both values correct, condone \(54 < \text{English} < 56\) but 54, 56 get A0
Median of English is larger than median of Maths
B1
Correct statement, median must be referenced within answer. No credit if statement references 'means'
Range Maths is 100 or IQ range Maths \(= 80 - 12 = 68\)
M1
Evidence of finding either both ranges or both IQ ranges i.e. see a minus
Range English is 60 or IQ range English \(= 62 - 42 = 20\)
A1
Both ranges or IQR correct
Maths marks have more spread than English marks
B1
Correct conclusion. Accept standard deviation but must see some figures
## Question 4:
| Answer | Mark | Guidance |
|--------|------|----------|
| Median Maths $= 40$ | M1 | Indication of finding medians, such as mark on graph or reference marks to 700 pupils, condone poor terminology such as 'mean' |
| Median English $= 55$ | A1 | Both values correct, condone $54 < \text{English} < 56$ but 54, 56 get A0 |
| Median of English is larger than median of Maths | B1 | Correct statement, median must be referenced within answer. No credit if statement references 'means' |
| Range Maths is 100 or IQ range Maths $= 80 - 12 = 68$ | M1 | Evidence of finding either both ranges or both IQ ranges i.e. see a minus |
| Range English is 60 or IQ range English $= 62 - 42 = 20$ | A1 | Both ranges or IQR correct |
| Maths marks have more spread than English marks | B1 | Correct conclusion. Accept standard deviation but must see some figures |
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4 The Mathematics and English A-level marks of 1400 pupils all taking the same examinations are shown in the cumulative frequency graphs below. Both examinations are marked out of 100 .\\
\includegraphics[max width=\textwidth, alt={}, center]{be6c6525-a20c-42d0-8fef-1cd254baaa76-06_1682_1246_404_445}
Use suitable data from these graphs to compare the central tendency and spread of the marks in Mathematics and English.\\
\hfill \mbox{\textit{CAIE S1 2019 Q4 [6]}}