# MEAN DEVIATION

Mean deviation :

Since range is based on only two observations, it is not regarded as an ideal measure of dispersion.

A better measure of dispersion is provided by mean- deviation which, unlike range, is based on all the observations.

For a given set of observation, mean-deviation 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 mean-deviation of x about an average A is given by For a grouped frequency distribution, mean-deviation about A is given by Where, N  =  ∑f

In most cases we take A as mean or median and accordingly, we get mean-deviation about mean or mean deviation about median.

## Coefficient of mean deviation

A relative measure of dispersion applying mean-deviation is given by Mean-deviation takes its minimum value when the deviations are taken from the median.

Also mean-deviation 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

## Properties of mean deviation

1)  Mean-deviation takes its minimum value when the deviations are taken from the median.

2)  Mean-deviation 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, mean-deviation does not possess mathematical properties.

## Mean-deviation - Practice problems

Problem 1 :

What is the mean-deviation about mean 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 mean-deviation about mean is given by

∑|x - x̄ | / n  =  10 / 6  =  1.67

Hence, mean-deviation for the given data is 1.67

Problem 2 :

Find mean-deviation about median and also the corresponding coefficient for the following observations.

82, 56, 75, 70, 52, 80, 68

Solution :

The given observations are in ascending order.

Number of observations  =  7

Median  =  (n+1) / 2  th value

Median  =  (7+1) / 2  th value

Median  =  8 / 2  th value

Median  =  4  th value

Median  =  70 Thus mean-deviation about median is given by

∑|x - median| / n  =  61 / 7  =  8.71

Hence, mean-deviation for the given data is 8.71

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

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

You can also visit the following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 