Question

A bus route take about 45 minutes . The company goal is a MAD of lss than 0.5 minute . One drivers time for 9 runs of the routere 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

Answer 1

Yes

Explanation:

The driver completed his route 9 different times as recorded here: 44.2, 44.9, 46.1, 45.8, 44.7, 45.2, 45.1, 45.3, and 44.6. The goal of the company is for the driver to complete it within less than 0.5 mins of 45 mins. The driver failed to do this two times when they completed it in 44.2 mins and 46.1 mins. If you take an average of the bus drivers 9 runs it is 45. 1 mins. Overall the driver does complete most runs within 0.5 mins on average.

44.2+ 44.9 +46.1 +45.8+ 44.7+ 45.2+ 45.1+ 45.3+ 44.6 = 405.9

405.9 / 9 = 45.1

Answer 2

The MAD driver reach is 0.4.

Yes the driver meet the goal.

Explanation:

Given : 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 router shown .

Time to complete bus routes (min)

44.2 44.9 46.1 45.8 44.7 45.2 45.1 45.3 44.6

To find : Did the bus driver meet the goal ?

Solution :

First we find out the mean of the data

Mean is defined as the sum of observation divided by total number of observation.

`\mu=(\sum x_n)/(n)`

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

`\mu=(405.9)/(9)`

`\mu=45.1`

The formula of mean deviation is given by,

`M=(\sum (x-\mu))/(N)`

Where,
`\mu=45.1` and x is the data given

Now, substitute the value in the formula,

`\sum x-\mu=(44.2-45.1)+(44.9-45.1)+(46.1-45.1)+(45.8-45.1)+(44.7-45.1)+(45.2-45.1)+(45.1-45.1)+(45.3-45.1)+(44.6-45.1)`

Values taken is always positive.

`M=(0.9+0.2+1+0.7+0.4+0.1+0+0.2+0.5)/(9)`

`M=(4)/(9)`

`M=0.4`

The company goal is a MAD of less than 0.5 minute.

The MAD driver reach is 0.4.

Therefore, Yes the driver meet the goal.