The traffic police recorded the speed (in km/hr) of 10 motorists as 47, 53, 49, 60, 39, 42, 55, 57, 52, 48. Later on an error in recording instrument was found. Find the correct average speed of the motorists if the instrument recorded 5 km/hr less in each case.

Given:

The traffic police recorded the speed (in km/hr) of 10 motorists as 47, 53, 49, 60, 39, 42, 55, 57, 52, 48.

Later on, an error in the recording instrument was found. 

The instrument recorded 5 km/hr less in each case.

To do:

We have to find the correct average speed of the motorists.

Solution:

We know that,

Mean $\overline{X}=\frac{Sum\ of\ the\ observations}{Number\ of\ observations}$

Total of speed of 10 motorists $= 47 + 53 + 49 + 60 + 39 + 42 + 55 +57 + 52 + 48$

$= 502$

Therefore,

Mean $(\bar{x})=\frac{\text { Total speed }}{10}$

$=\frac{502}{10}$

$=50.2 \mathrm{~km} / \mathrm{h}$

Error in recording $=5 \mathrm{~km} / \mathrm{hr}$ less in each case.

This implies,

Actual mean speed $=50.2+5$

$=55.2 \mathrm{~km} / \mathrm{h}$

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Updated on: 10-Oct-2022

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