Question

The table shows the scores of 10 students in Mr. Garcia’s 3rd period math class on their last 20-point quiz.

Name Quiz Score

Kelsey 18

Adam 12

Matthew 15

Maria 10

Victoria 13

Michael 20

Jessica 16

Anna 12

Brandon 18

Luis 6


What is the absolute deviation of Victoria’s quiz score from the mean?


A. 0 points


B. 2 points


C. −1 point


D. 1 point
Please give the right answer

Answer 1

B. 2 points

(Approximately)

Explanation:

The mean absolute deviation (MAD) is defined as

`MAD=(\Sigma |x_(i)-\mu| )/(N)`

Where
`\mu` is the means and
`N` is the total number of elements.

First, we need to find the mean:

`\mu = (\Sigma x_(i) )/(N) =(18+12+15+10+13+20+16+12+18+6)/(10)= (140)/(10)\\ \mu=14`

Then, we calculate the difference between each value and the mean, from that difference, we are gonna use the absolute value.

18 - 14 = |4|

12 - 14 = |-2|

15 - 14 = |-1|

10 - 14 = |-4|

13 - 14 = |-1|

20 - 14 = |6|

16 - 14 = |2|

12 - 14 = |-2|

18 - 14 = |4|

6 - 14 = |-8|

Now, we sum all terms and divide them by the total number of elements, which are 14.

`MAD=(4+2+1+4+1+6+2+2+4+8)/(14)= (34)/(14)\\ MAD \approx 2.4`

Therefore, the absolute deviation is about 2 points. The right answer is B.