Question

Dora calculated the mean absolute deviation for the data set 35, 16, 23, 42, and 19. Her work is shown below.

Step 1: Find the mean.


mean = Start Fraction 35 + 16 + 23 + 42 + 19 Over 5 End Fraction = 27


Step 2: Find each absolute deviation.


8, 11, 4, 15, 8


Step 3: Find the mean absolute deviation.


M A D = Start Fraction 8 + 11 + 4 + 15 Over 5 End Fraction = 9.5


What is Dora’s error?

Answer 1

D. Dora used only four numbers in finding the mean absolute deviation.

Explanation:

EDGE 2020

Answer 2

The calculation in step 3 is wrong

Explanation:

1) The mean of a dataset is given by the sum of the values of the dataset divided by the number of values.

In this problem, the dataset is

35, 16, 23, 42, 19

And the number of data is

N = 5

So the mean is

`\bar x=(35+16+23+42+19)/(5)=27`

So, step 1 is correct.

2)

The absolute deviation of a value in the dataset is the absolute value of its difference from the mean value:

`\sigma_i = |x_i-\bar x|`

Since here the mean value is

`\bar x=27`

Then for each of the values in this dataset, we have:

`\sigma_(1)=|35-27|=8\\\sigma_(2)=|16-27|=11\\\sigma_(3)=|23-27|=4\\\sigma_(4)=|42-27|=15\\\sigma_(5)=|19-27|=8`

So calculations in step 2 are also correct.

3)

The mean absolute deviation is given by the sum of the absolute deviations for each data divided by the number of values in the dataset.

Therefore in this problem, it is:

`\bar \sigma = (\sum \sigma_i)/(N)=(8+11+4+15+8)/(5)=9.2`

While the result reported by Dora is 9.5: therefore, this step is not correct.