Download ∑ MAD Deviation µ

Comparing the Mean Absolute Deviation (MAD) and the Standard
Deviation
Here is the data: 13, 14, 24, 24, 25, 26
1. Find the mean, median and mode for this data.
2. Use the table to find the MAD =
Value of x
Deviation
x-µ
∑ x−µ
n
, the Mean Absolute Deviation of the data.
Absolute Deviation
x−µ
13
14
24
24
25
26
Total
MAD =
∑ x−µ
n
= _________
3. Now find the standard deviation of the data.
Value of x
Deviation
x-µ
Squared Deviation
(x – µ)2
13
14
24
24
25
26
Total
The population standard deviation is given by the formula:
σ=
(x − µ)2
= __________
n
While I think that the MAD is a more “natural” way to measure deviation, we use the
standard deviation in statistics. This is basically because it is easier mathematically to
deal with squares and square roots than it is to deal with absolute values.
Top 10 Reasons Why We Use the Standard Deviation as Our Measure of Variation
(by Ann E. Watkins, California State University Northridge)
10. Every value gets taken into account.
9. In important distributions, the formula for the SD turns out to be short and sweet.
8. It is easy to compute with squares.
7. The SD has a rather intimate relationship with the mean so if the mean is the
measure of center, the SD is the logical measure for spread.
6.The SD and the mean have a rather intimate relationship with the normal
distribution
5.The SD goes someplace mathematically. The MAD is reasonable, but it isn’t
important.
4. Standard deviations add like Pythagoras.
3. The formula for the SD looks suspiciously like the Euclidean distance formula.
2. The SD is a distance!
1. It must be the official one to use since it is called the “standard” deviation
0. The SD is on the calculator and the MAD is not.
Population Standard Deviation:
σ=
(x − µ)2
n
Sample Standard Deviation:
s=
(x − µ)2
n −1