The following table shows the classification of number of vehicles and their speeds on Mumbai - Pune expressway. Find the median of the data .

Answer

The median of the data is 75 vehicles.

Explanation

The classes ( Average speed of vehicles) in the table are not continuous.
To find the median, the classes must be continuous.
The difference between the upper class limit of a class and the lower class limit of it succeeding class is 1.
`:. ` subtract ` 1 div 2 = 0.5` from the lower class limit of each class and add `0.5` to the upper class limit of each class.
Make a column of cf ( less than type) in the new table showing the continuous classes.

Here, total of frequencies `N = Sigma f_(i) = 200`.
` :. N/2 = 200/2 = 100`
Cumulative frequency which is greater than 100 is 184.
` :. ` the corresponding continuous class ` 74.5 - 79.5` is the median class.
`L = 74.5, f = 85, cf = 99, h = 5`
Median ` = L + [(N/2 - cf)/f] xx h`
` = 74.5 + (100 - 99)/85 xx 5`
` = 74.5 + 1/17`
` = 74.5 + 0.06` (Approx.)
` = 74.56`
But the number of vehicles cannot be in fraction
So, ` 74 .56 approx 75`.