Question

What is the mean absolute deviation of following set of data? 4 6 12 8 10 10 6 8

Answer 1

Mean :-

Sum of all observations / no. of observations

Here given observations are 4,6,12,8,10,10,6,8

Mean = 4+6+12+8+10+10+6+8/8

=64/8

=8

Mean of the given observations is 8

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Answer 2

Concept:

Standard deviation is a measure of dispersion, a measure of how much the values in a set of data are likely to differ from their mean value. The absolute value is used to avoid deviations with opposite signs canceling each other out.

Find:

We have find the mean absolute deviation

Given:

4 6 12 8 10 10 6 8

Step by step explain:

Standard deviation is a measure of dispersion, a measure of how much the values in a set of data are likely to differ from their mean value. The absolute value is used to avoid deviations with opposite signs canceling each other out.

The mean absolute deviation of the collected data set is the average of the absolute deviations from the center of the data set. Mean Absolute Deviation, abbreviated as MAD, has four types of deviations, which are derived by central tendency, mean median and mode, and standard deviation. However, it is best to use the mean absolute deviation because it is more accurate and easier to use in real-world situations.

$mean = \frac{sum \: of \: all \: observation}{no \: of \: observation}$

$mean = \frac{4 + 6 +12 + 8 + 10 + 10 + 6 + 8 }{8}$

$mean = \frac{64}{8}$

$mean = 8$

Deviation of mean are:

(4-8, 6-8, 12-8, 8-8, 10-8, 10-8, 6-8, 8-8)

(-4, -2, 4, 0, 2, 2 ,-2, 0)

$absolute \: mean = \frac{ - 4 - 2 + 4 + 2 + 2 - 2}{6}$

$absolute \: mean = \frac{0}{6}$

absolute mean=0

Hence the mean absolute deviation is 0

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