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Calculate arithmetic mean using direct method for the following data shows distance covered by $125$ buses to perform its duty.

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23.1 / km

23.6 / km

30.5 / km

34.2 / km

answer is C.

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Detailed Solution

Given data,
Question Image

To calculate the arithmetic mean, we will be using direct method.
Now, let’s represent the data into frequency distribution table

Distance $(x_{i})$	No. of buses $(f_{i})$	$f_{i} x_{i}$
$50$	$5$	$250$
$45$	$15$	$675$
$35$	$25$	$875$
$20$	$35$	$700$
$10$	$45$	$450$

Then,

Σ f_{i} = 5 + 15 + 25 + 35 + 45

\Rightarrow Σ f_{i} = 125

Σ f_{i} x_{i} = 250 + 675 + 875 + 700 + 450

\Rightarrow Σ f_{i} x_{i} = 2950

The mean will be,

∴ mean = \frac{Σ f_{i} x_{i}}{Σ f_{i}}

\Rightarrow mean = \frac{2950}{125}

\Rightarrow mean = 23.6

So, the distance covered by

25

buses is

23.6 km

.
Hence, the correct option is 3.

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