Question

A bus route takes about 45 minutes. The company's goal is MAD of less than 0.5 minutes. One drive's times for 9 runs of the route are shown. Did the bus driver meet the goal?

Answer 1

A bus route take about 45 minutes . The company goal is a MAD of less than 0.5 minute . One drivers time for 9 runs of the route are shown . Did the bus driver meet the goal ? Time to complete bus routes (min) 44.2 44.9 46.1 45.8 44.7 45.2 45.1 45.3 44.6

Yes the driver meets the goal.

The mean values is 45.1 and MAD value is 0.4

Explanation:

Given:

Minimum time to complete bus routes (x) :

44.2, 44.9, 46.1, 45.8, 44.7, 45.2, 45.1, 45.3, 44.6.

We have to find mean and mean average deviation [MAD] values.

Mean,
`(\bar x)` =
`(\sum x)/(n)` ...Ratio of sum of all observations and no. of observations.

⇒
`\bar x =(44.2+44.9+46.1+45.8+44.7+45.2+45.1+45.3+44.6)/(9)`

⇒
`\bar x =(405.9)/(9)`

⇒
`\bar x =45.1` minutes

Lets find the MAD values.

⇒ MAD =
`(\sum\left |x-\bar x\right |)/(n)`

⇒
`(\sum\left |x-\bar x\right |)/(n)`

⇒
`(\sum\left |44.2-45.1\right |+\left |44.9-45.1\right|+\left |46.1-45.1\right |+\left |45.8-45.1\right |+\left|44.7-45.1\right |+\left|45.2-45.1\right |+\left|45.1-45.2\right |+\left|45.3-45.1\right |+\left|44.6-45.1\right |)/(9)`⇒
`(0.9+0.2+1+0.7+0.4+0.1+0+0.2+0.5)/(9)`

⇒
`(4)/(9)`

⇒
`0.4` minutes

The company's goal is less than 0.5 and we can see tat our MAD value is less than 0.5 that is 0.4.

So the bus driver meets the goal.

Mean value is 45.1 and MAD value is less than 0.5 minutes