**Mean Absolute Deviation (MAD) :**

A measure of variability is a single number used to describe the spread of a data set. It can also be called a measure of spread. One measure of variability is the mean absolute deviation (MAD), which is the mean of the distances between the data values and the mean of the data set.

For a given set of observation, MAD is defined as the arithmetic mean of the absolute deviations of the observations from an appropriate measure of central tendency.

Let the variable "x" assume "n" values as given below

Then the MAD of x is given by

For a grouped frequency distribution, MAD is given by

Where, N = ∑f

A relative measure of dispersion applying MAD is given by

MAD takes its minimum value when the deviations are taken from the median.

Also MAD remains unchanged due to a change of origin but changes in the same ratio due to a change in scale

i.e. if y = a + bx, a and b being constants,

then MD of y = |b| × MD of x

1) MAD takes its minimum value when the deviations are taken from the median.

2) MAD remains unchanged due to a change of origin but changes in the same ratio due to a change in scale

i.e. if y = a + bx, a and b being constants,

then MD of y = |b| × MD of x

3) It is rigidly defined

4) It is based on all the observations and not much affected by sampling fluctuations.

5) It is difficult to comprehend and its computation

6) Furthermore, unlike SD, MAD does not possess mathematical properties.

**Problem 1 : **

What is the MAD for the following numbers?

5, 8, 10, 10, 12, 9

**Solution :**

The mean is given by

x̄ = (5 + 8 + 10 + 10 + 12 + 9) / 6

x̄ = 54 / 6

x̄ = 9

Thus MAD is given by

∑|x - x̄ | / n = 10 / 6 = 1.67

Hence, MAD for the given data is 1.67

**Problem 2 : **

The data represent the height, in feet, of various buildings. Find the mean absolute deviation.

60, 58, 54, 56, 63, 65, 62, 59, 56, 57

**Solution :**

Let x = 60, 58, 54, 56, 63, 65, 62, 59, 56, 57

The mean is given by

x̄ = (60+58+54+56+63+65+62+59+56+57) / 10

x̄ = 590 / 10

**x****̄**** = 59**

Absolute deviations of observations from mean :

|60 - 59 | = |1| = 1

|58 - 59 | = |-1| = 1

|54 - 59 | = |-5| = 5

|56 - 59 | = |-3| = 3

|63 - 59 | = |4| = 4

|65 - 59 | = |6| = 6

|62 - 59 | = |3| = 3

|59 - 59 | = |0| = 0

|56 - 59 | = |-3| = 3

|57 - 59 | = |-2| = 2

Calculate the MAD by finding the mean of the above absolute deviations of observations from mean. Round to the nearest whole number.

MAD = (1+1+5+3+4+6+3+0+3+2) / 10

MAD = 28 / 10

MAD = 2.8 ≈ 3

After having gone through the stuff given above, we hope that the students would have understood "MAD".

Apart from the stuff given above, if you want to know more about "Mean absolute deviation", please click here

Apart from the stuff given on this web page, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**