STA 301 –
STATISTICS AND PROBABILITY
Notes of Lecture
11
Mean Deviation,
Standard Deviation and Coefficient of Variation
Mean Deviation:
- Complete name of mean deviation is mean absolute deviation
- Absolute dispersion: is a pure number and compare variability of two or more data sets.
- Mean deviation is that – to measure the dispersion around arithmetic mean.
- Compute distance of x value from the mean (x-x)
- Is it important of x-x? As sum of x-xbar to be zero, it means overall dispersion of x values from mean is zero.
- So this not correct because there is variability of x around mean.
- Solution of this is to take absolute values x-x.
- Frequency distribution of continuous variable
a.
Compute mid-point of every class X =
(a+b)/2
b.
Arithmetic mean = sigma fx/sigmaf
- Graphical representation of MD
a. Range
horizontal line segment start from x0 and going upto xm
b. Quartile
deviation half horizontal distance between first quartile and third quartile
c. MD
or SD we measure the horizontal spread of our distribution
Standard Deviation:
- The step of absolute is not defendable from mathematical point of view so this formula of MD is not preferable formula. To overcome this problem we introduce the SD
- Relative measure of dispersion corresponding to MD: MD/mean
- When data have very low and very high data then better to use median to calculate the average instead of arithmetic mean.
- SD is the most important and widely used to measure of dispersion.
- We squared the deviation.
- Adding squares of deviation from mean dividing by number of observation is called variance.
- Variance expressed in square units.
- Positive Square root of variance is called the SD
- Unit of SD is same as data units
- Coefficient of variation is percentage
- We can compare the variability of two different dataset even the unit are different.
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