The production of electric bulbs in different factories is shown in the following table. Find the median of the productions.
| No. of bulbs produced (Thousands) | 30–40 | 40–50 | 50–60 | 60–70 | 70–80 | 80–90 | 90–100 |
|---|---|---|---|---|---|---|---|
| No. of factories | 12 | 35 | 20 | 15 | 8 | 7 | 8 |
Answer: Median = 52.75 thousand, i.e. 52,750 bulbs
| Class | Frequency | Cumulative frequency (less than) |
|---|---|---|
| 30–40 | 12 | 12 |
| 40–50 | 35 | 47 |
| 50–60 | 20 | 67 |
| 60–70 | 15 | 82 |
| 70–80 | 8 | 90 |
| 80–90 | 7 | 97 |
| 90–100 | 8 | 105 |
\(N = 105\), so \(\frac{N}{2} = 52.5\). The first cumulative frequency greater than or equal to 52.5 is 67, so the median class is 50–60.
\(L = 50\), \(cf = 47\), \(f = 20\), \(h = 10\)
\[ \text{Median} = L + \left[\frac{\frac{N}{2} - cf}{f}\right] \times h \]
\[ = 50 + \frac{52.5 - 47}{20} \times 10 \]
\[ \approx 52.75 \]
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