A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mean and median of the following data.

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Question

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mean and median of the following data.

| Number of cars | $0 - 10$ | $10 - 20$ | $20 - 30$ | $30 - 40$ | $40 - 50$ | $50 - 60$ | $60 - 70$ | $70 - 80$ |
|---|---|---|---|---|---|---|---|---|
| Frequency (periods) | $7$ | $14$ | $13$ | $12$ | $20$ | $11$ | $15$ | $8$ |

Accepted Answer

Step 1: | Number of cars | $x_i$ | $f_i$ | $x_i f_i$ | c.f. |
|---|---|---|---|---|
| $0 - 10$ | $5$ | $7$ | $35$ | $7$ |
| $10 - 20$ | $15$ | $14$ | $210$ | $21$ |
| $20 - 30$ | $25$ | $13$ | $325$ | $34$ |
| $30 - 40$ | $35$ | $12$ | $420$ | $46$ |
| $40 - 50$ | $45$ | $20$ | $900$ | $66$ |
| $50 - 60$ | $55$ | $11$ | $605$ | $77$ |
| $60 - 70$ | $65$ | $15$ | $975$ | $92$ |
| $70 - 80$ | $75$ | $8$ | $600$ | $100$ |
| Total | | $100$ | $4070$ | |
Step 2: Mean $= \frac{\sum x_i f_i}{\sum f_i} = \frac{4070}{100} = 40.7$
Step 3: Median class: $40 - 50$ ($\frac{N}{2} = 50$, c.f. just exceeding 50 is 66)
Step 4: Median $= 40 + \frac{50 - 46}{20} 	imes 10 = 40 + 2 = 42$

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Solution