Question

The SAT scores for a group of 10 students are shown. What is the mean absolute deviation of the group?

A. 45
B. 88
C. 880
D. 1532

Answer 1

B. 88

Explanation:

First find the mean:

Add up the values to find the mean of the data set:

1520 + 1630 + 1480 + 1580 + 1400 + 1300 + 1700 + 1610 + 1580 + 1520 = 15320

Divide 15320 by 10 because there are 10 numbers in the data set:

`(15320)/(10) = 1532`

Subtract the numbers of the data set by the mean:

1520 - 1532 = -12

1630 - 1532 = 98

1480 - 1532 = -52

1580 - 1532 = 48

1400 - 1532 = -132

1300 - 1532 = -232

1700 - 1532 = 168

1610 - 1532 = 78

1580 - 1532 = 48

1520 - 1532 = -12

The mean deviation is always positive so change the negatives to positives. After that, add them up:

12 + 98 + 52 + 48 + 132 + 232 + 168 + 78 + 48 + 12 = 880

Divide 880 by 10 because there are 10 numbers in the data set:

`(880)/(10) =88`

The mean absolute deviation is 88

Answer 2

Mean is the average of a given set of numbers in a distribution. It is given by dividing the sum of the values in the distribution by the number of values. In this case;
The total numbers are 10
The sum of the numbers is 15320
Therefore, mean= 15320/10 = 1532
Hence the mean is 1532
Then the absolute deviations from the mean for all the values will be; (given by;
(x1-xm),(x2-xm), .........(xn-xm) where xm is the mean)
=12,98,52,48,132,232,168,78,48,12
Sum of the absolute deviations = 880
Mean absolute deviation = 880/10 = 88
Therefore, the mean absolute deviation is 88