The frequency distribution table shows the number of mango trees in a grove and their yield of mangoes. Find the median of data.
| No. of Mangoes | 50–100 | 100–150 | 150–200 | 200–250 | 250–300 |
|---|---|---|---|---|---|
| No. of trees | 33 | 30 | 90 | 80 | 17 |
Answer: Median ≈ 184.44, i.e. about 184 mangoes
| Class | Frequency | Cumulative frequency (less than) |
|---|---|---|
| 50–100 | 33 | 33 |
| 100–150 | 30 | 63 |
| 150–200 | 90 | 153 |
| 200–250 | 80 | 233 |
| 250–300 | 17 | 250 |
\(N = 250\), so \(\frac{N}{2} = 125\). The first cumulative frequency greater than or equal to 125 is 153, so the median class is 150–200.
\(L = 150\), \(cf = 63\), \(f = 90\), \(h = 50\)
\[ \text{Median} = L + \left[\frac{\frac{N}{2} - cf}{f}\right] \times h \]
\[ = 150 + \frac{125 - 63}{90} \times 50 \]
\[ \approx 184.44 \]
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