The prices of different articles and demand for them is shown in the following frequency distribution table. Find the median of the prices.
| Price (Rupees) | 20 less than | 20–40 | 40–60 | 60–80 | 80–100 |
|---|---|---|---|---|---|
| No. of articles | 140 | 100 | 80 | 60 | 20 |
Answer: Median price = ₹ 32
'Less than 20' is taken as the class 0–20.
| Class | Frequency | Cumulative frequency (less than) |
|---|---|---|
| 0–20 | 140 | 140 |
| 20–40 | 100 | 240 |
| 40–60 | 80 | 320 |
| 60–80 | 60 | 380 |
| 80–100 | 20 | 400 |
\(N = 400\), so \(\frac{N}{2} = 200\). The first cumulative frequency greater than or equal to 200 is 240, so the median class is 20–40.
\(L = 20\), \(cf = 140\), \(f = 100\), \(h = 20\)
\[ \text{Median} = L + \left[\frac{\frac{N}{2} - cf}{f}\right] \times h \]
\[ = 20 + \frac{200 - 140}{100} \times 20 \]
\[ \approx 32 \]
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