Discussion
The ogive more than and ogive less than of the following grouped data
| Class | Frequency |
|---|---|
| 0-8 | 8 |
| 8-20 | 12 |
| 20-30 | 18 |
| 30-35 | 10 |
| 35-40 | 4 |
intersect at which of the following points ?
Answer: B
The ogives intersect at 23.33, the median.
The 'less than' and 'more than' ogives cross at the median. The total frequency is N = 52, so N/2 = 26. The cumulative frequencies are 8, 20, 38, 48, 52, so the median class is 20-30, with lower limit 20, cumulative frequency before it 20, frequency 18 and width 10:
\[ \begin{aligned} \text{Median} &= 20 + \frac{26 - 20}{18} \times 10 \\ &= 20 + 3.33 = 23.33 \end{aligned} \]
The nearby values 23.00, 23.67 and 24.00 come from rounding or from using the wrong cumulative frequency or class width.
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