Question

The computer in a police car records the distance the car travels in both miles and kilometers. (1 mile is approximately equal to 1.6 km). Think about the travel data from one police car for a year. If we calculate the standard deviation of the distances in miles and also in kilometers, which of the following statements is true?
1. The standard deviation of the distances in miles is larger.
2. The standard deviation of the distances in kilometers is larger.
3. The standard deviations are the same.

Answer 1

Answer:

2. The standard deviation of the distances in kilometers is larger.

Step-by-step explanation:

Let us assume the distance of car travel in miles is x

And, the  distance of car travel in kilometers is y

Given that

1 mile = 1.6 km

That means

y = 1.6x

Therefore

The standard deviation of y =  1.6 × (standard deviation of x)

The above equation represents

The standard deviation of y > standard deviation of x

hence, the correct option is 2.