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 overage speed of the motorists if the instrument recorded 5 km/hr less in each case.

Open in App

Solution

Given that the recorded speed (in km/hr) of 10 motorists are 47, 53, 49, 60, 39, 42, 55, 57, 52, and 48. Let us denote the speeds of 10 motorists by.

Ifbe the mean of the n observations, then we have

Hence we have

This mean is incorrect. We have to find the correct mean.

It was found that the instrument recorded 5 km/hr less in each case.

To get the correct we have to add 5 with each entry. Then the correct entries are

Recall that ifbe the mean of the n observationsand if we add a constant k with each of the observations, then the new mean becomes

Therefore the correct mean speed of the motorists is

Suggest Corrections

Similar questions

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 error in recording instrument was found.Find the correct average of the motorists if the instrument recorded 5 km/hr less in each case.

Q. The traffic police recorded the speed (in km/h) of

10

motorists as

47

53

49

60

39

42

55

57

52

48

. Later on an error in the recording instrument was found. Find the correct average speed of the motorists if the instrument recorded the speed

5

km/h less in each case.

Q. A person recorded the speed (in km/hr) of 10 motorists as 48, 52, 57, 55, 45, 39, 61, 49, 51 and 43. The average speed of the motorists is

Q. A person recorded the speed (in km/hr) of 10 motorists as 48, 52, 57, 55, 45, 39, 61, 49, 51 and 43. Find the average speed of the motorists.

Join BYJU'S Learning Program