The following table shows the classification of number of vehicles and their speeds on Mumbai-Pune express way. Find the median of the data.
| Average Speed of Vehicles (Km/hr) | 60–64 | 64–69 | 70–74 | 75–79 | 79–84 | 84–89 |
|---|---|---|---|---|---|---|
| No. of vehicles | 10 | 34 | 55 | 85 | 10 | 6 |
Answer: Median speed ≈ 74.56 km/hr
The classes as printed (60–64, 64–69, ..., 79–84, 84–89) are clearly meant to be 60–64, 65–69, 70–74, 75–79, 80–84, 85–89 (each of width 5). These are not continuous, so subtract 0.5 from lower limits and add 0.5 to upper limits.
| Class | Frequency | Cumulative frequency (less than) |
|---|---|---|
| 59.5–64.5 | 10 | 10 |
| 64.5–69.5 | 34 | 44 |
| 69.5–74.5 | 55 | 99 |
| 74.5–79.5 | 85 | 184 |
| 79.5–84.5 | 10 | 194 |
| 84.5–89.5 | 6 | 200 |
\(N = 200\), so \(\frac{N}{2} = 100\). The first cumulative frequency greater than or equal to 100 is 184, so the median class is 74.5–79.5.
\(L = 74.5\), \(cf = 99\), \(f = 85\), \(h = 5\)
\[ \text{Median} = L + \left[\frac{\frac{N}{2} - cf}{f}\right] \times h \]
\[ = 74.5 + \frac{100 - 99}{85} \times 5 \]
\[ \approx 74.56 \]
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