Question

In the past 6 days, Adrion's travel time to school has varied: 22 minutes, 27 minutes, 34 minutes, 29 minutes, 20 minutes, and 18 minutes. The work shown is her calculation of the mean absolute deviation of the time traveled. Which step contains the first error Adrion made?

Answer 1

Step 4, because she should have divided rather than subtracting 6.

Explanation:

The mean absolute deviation formula,

`MAD=(\sum |x-\mu|)/(n)`

Where,

`\mu` represents mean,

n represents the number of items,

x represents an item,

Here, data items are,

22, 27, 34, 29, 20, and 18

Thus, the steps for finding the mean absolute deviation are as follows,

Step 1 : Finding means,

`(22+27+34+29+20+18)/(6)=25`

Step 2 : absolute values of the given data items,

`|22-25|=3,`
`|27-25|=2,`
`|34-25|=9,`
`|29-25|=4,`
`|20-25|=5,`
`|18-25|=7`

Step 3 : Sum of all absolute values,

`3+2+9+4+5+7=30`

Step 4 : Divide sum of absolute value by number of data items,

`(30)/(6)=5`

Hence, step 4 contains the first error, because she should have divided rather than subtracting 6.

Answer 2

I think she made a mistake at step 4 because I know in order to find the mean absolute deviation of a number you must divide as the last step, not subtract and the rest of her work looks correct.