Question

The following box plot represent the time taken to travel from home to the gym using motorcycle and the car.
Using the data, choose the correct statement from the given options.

• A. The difference in time taken by the motorcycle and the car to reach the gym is significantly higher
• B. Both can reach the gym in equal time
• C. IQR of Motorcycle is not equal to IQR of Car
• D. The difference in time taken by the motorcycle and the car to reach the gym is not much.

Answer 1

The correct option is D The difference in time taken by the motorcycle and the car to reach the gym is not much.


For motorcycle:
Median = 65
Median of lower half (Q1) = 55
Median of upper half(Q3) = 70
IQR = Q3-Q1
= 70-55 = 15

For car:

Median = 80
Median of lower half (Q1) = 75
Median of upper half(Q3) = 90
IQR = Q3-Q1
= 90-75 = 15
Here,
IQR(motorcycle) = IQR(car)

When two data distributions have similar variabilities, we can compare them by writing the difference in the measures of center as a multiple of the measure of variability.
So,
Difference in median = 80 - 65 = 15
IQR = 15
Ratio of difference in the median to IQR for the given data = 1

Since, 1 < 2 the difference in time taken by the motorcycle and the car is not much.