States that experience four seasons tend to have more issues with potholes becau

Question

States that experience four seasons tend to have more issues with potholes because of the changes in temperature and variety of precipitation. The Department of Transportation for Michigan is considering how much money they need to allocate to ensure the states roads are safe for travel. Theyve taken a random sample of 500 roads from the state and then selected a random mile of that road to evaluate for repairs. On each mile stretch, theyve recorded the length (in meters) that requires repairs. Below is the distribution table for the length in meters in need of repair:

What is the estimate for the median length of road in need of repair?

Length 0-5 5-10 10-12 12-20 20-40 Count 217 176 54 38 15

Explanation / Answer

Cumulative frequency table will be:

(500/2)th observative i.e. 225th observation lies in 5 - 10. So, median class will be 5 -10.

Median = 5 + (225 - 217)/176 * 5 = 5.227 [Rounded off to 3 decimal places]

Length Count Cumulative Count 0 - 5 217 217 5 - 10 176 217 + 176 = 393 10 - 12 54 393 + 54 = 447 12 - 20 38 447 + 38 = 485 20 - 40 15 485 + 15 = 500

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