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What is the arithmetic mean using direct method for the following data shows distance covered by $120$ passengers to perform their regular work?

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20 km

25 km

22 km

15 km

answer is B.

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Detailed Solution

It is given the data shows distance covered by

120

passengers to perform their regular work.
Question Image

We convert the data in terms of the following expression.

x_{i} = \frac{lower limit + upper limit}{2}

Distance	$x_{i}$	$(f_{i})$	${(x}_{i}) \times (f_{i}) = (x_{i} f_{i})$
5 - 15	10	30	300
15 - 20	17.5	20	350
20 - 35	27.5	30	825
35 - 40	37.5	40	1500
		$Σ f_{i} = 120$	$Σ f_{i} x_{i} = 2975$

From the table, we get

Σ f_{i} = 120

Σ f_{i} x_{i} = 2975

We know that,
Mean =

\frac{Σ f_{i} x_{i}}{Σ f_{i}}

\Rightarrow Mean = \frac{2975}{120}

\Rightarrow Mean = 24.79 \approx 25

Thus, the average of the data is 25 km.
Hence, the correct option is 2.

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