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3 years ago

Which measure best represents the spread of the data shown below and what is its value? 10, 9, 8, 30, 7, 8, 9, 6, 7, 11

1 answer:

4 0

Lets put the numbers in order...
6,7,7,8,8,9,9,10,11,30

Q1 = 7
Q2 = (8 + 9) / 2 = 17/2 = 8.5
Q3 = 10
IQR = Q3 - Q1 = 10 - 7 = 3 <== so the interquartile range is 3

mean absolute deviation...
the mean of our data is 10.5

now we subtract the mean from every data point....and find its absolute value

6 - 10.5 = -4.5.....| -4.5| = 4.5
7 - 10.5 = -3.5.....| -3.5| = 3.5
7 - 10.5 = -3.5.....|-3.5| = 3.5
8 - 10.5 = - 2.5....|-2.5| = 2.5
8 - 10.5 = -2.5....|-2.5| = 2.5
9 - 10.5 = -1.5....|-1.5| = 1.5
9 - 10.5 = -1.5....|-1.5| = 1.5
10 - 10.5 = -0.5..| -0.5| = 0.5
11 - 10.5 = 0.5...|0.5| = 0.5
30 - 10.5 = 19.5..|19.5| = 19.5

now we take the average of these numbers
(4.5+3.5+3.5+2.5+2.5+1.5 + 1.5 + 0.5+0.5+19.5) / 10 =
40/10 = 4 <== ur mean absolute deviation

In summary :
ur interquartie range (IQR) of ur data set is 3
ur mean absolute deviation (MAD) of ur data set is 4

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