The table below shows the frequency distribution of the marks scored by fifty students in an examination. Marks (%) 0-9 10-19 20-29 30-39 40-49 50-59 60-69 ...
Question 1 Report
The table below shows the frequency distribution of the marks scored by fifty students in an examination.
| Marks (%) | 0-9 | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 | 60-69 | 70-79 | 80-89 | 90-99 |
| Freq | 2 | 3 | 4 | 6 | 13 | 10 | 5 | 3 | 2 | 2 |
(a) Draw the cumulative frequency curve for the distribution.
(b) Use your curve to estimate the : (i) upper quartile; (ii) pass mark if 60% of the students passed.
Answer Details
(a) Cumulative frequency table
| Marks (%) | Upper class boundary | Frequency | Cumulative frequency |
|---|---|---|---|
| 0–9 | 9.5 | 2 | 2 |
| 10–19 | 19.5 | 3 | 5 |
| 20–29 | 29.5 | 4 | 9 |
| 30–39 | 39.5 | 6 | 15 |
| 40–49 | 49.5 | 13 | 28 |
| 50–59 | 59.5 | 10 | 38 |
| 60–69 | 69.5 | 5 | 43 |
| 70–79 | 79.5 | 3 | 46 |
| 80–89 | 89.5 | 2 | 48 |
| 90–99 | 99.5 | 2 | 50 |
Plot the cumulative frequencies against the upper class boundaries, beginning with \\((-0.5,0)\\) , and join the points with a smooth increasing curve.
(b)(i) Upper quartile
\[\frac{3N}{4}=\frac{3(50)}{4}=37.5.\]
From the curve, the mark corresponding to cumulative frequency \(37.5\) is approximately \(57\).
\[\boxed{Q_3\approx57\text{ marks}}\]
(b)(ii) Pass mark when 60% passed
Number who passed \(=0.60\times50=30\). Hence the number below the pass mark is \(50-30=20\).
From the curve, the mark corresponding to cumulative frequency \(20\) is approximately \(42\).
\[\boxed{\text{Pass mark}\approx42\text{ marks}}\]
Download The App On Google Playstore
Everything you need to excel in your exams
