Calculate the mean absolutee deviation (MAD) MAD= 2+3+4+4+4+5+5+6+6+6+7+8

Question

I am im 7th grade and this is what we are doing in class. I have tried multiple times and the MAD does not make sense.

Answer 1

sum of 60 divided by 12 numbers = 60/12 = 5 = mean or arithmetic average

it's also the median

absolute deviation from the mean is necessarily = 0

2 is 3 below

3 is 2 below

4 is 1 below

those deviations sum to -3-2-1-1-1 = -8

6 is 1 above

7 is 2 above

8 is 3 above

those deviations sum to 1+1+1+2+3 = 8

-8+8=0

0/12 = 0

this is always true, & not very helpful, no matter what numbers you use

so they ignore the negative signs and use the absolute values of each deviation

then

|8|+|-8|= 8+8=16

divide by 12

MAD = 16/12 = 4/3 = 1 1/3 = 1.333...

another way to get rid of the negative signs is square the deviations

then the deviations squared are

3^2 = 9 = (-3)^2

2^2 = 4 = (-2)^2

1^2 = 1 = (-1)^2

sum of squared deviations = 9+4+1+1+1+1+1+1+4+9 = 22

divide by n = number of numbers = 12 if it's the entire population, or by n-1 = 11, if it's a sample of a larger population

22/12 = 11/6

22/11 = 2

take the square root

sqr(11/6) or sqr2

= about 1.354 for n=12

or = 1.414 for n-1 = 11

that's the standard deviation, SD, or the symbol is the small greek letter sigma or just the english s

MAD with 4/3 or 1.333... is very close to the population standard deviation, but MAD is always < SD

both are measures of dispersion of the data

MAD gives the expected value. SD gives more weight to larger deviations, and is based on a normal (bell shaped) curve, so it's larger

they really teach this in 7th grade? That could drive you crazy or MAD. Or maybe your instructor is MAD too.