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# Moments - Measures of Dispersion, Business Mathematics & Statistics B Com Notes | EduRev

Created by: Arshit Thakur

## B Com : Moments - Measures of Dispersion, Business Mathematics & Statistics B Com Notes | EduRev

The document Moments - Measures of Dispersion, Business Mathematics & Statistics B Com Notes | EduRev is a part of the B Com Course Business Mathematics and Statistics.
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• Moments

A moment designates the power to which deviation are raised before averaging them.

Methods of Standard Deviation
1. Moments about Mean or Central Moments
2. Moments about Origin or Zero
3. Moments about Provisional Mean or Arbitrary Value (Non Central Moment)

1. Moments about Mean or Central Moments

For Ungrouped Data​ For Grouped Data​ 2. Moments about Origin or Zero  For Grouped Data 3. Moments about Provisional Mean or Arbitrary Value (Non Central Moment)
4. Methods of Standard Deviation

i. Direct Method
ii. Short Cut Method
iii. Coding Method or Step-Deviation Method

i. Direct Method For Ungrouped Data

For Ungrouped Data Where A is constant For Grouped Data Where A is constant ii. Short Cut Method
For Ungrouped Data Where D= X - A  Where D= X - A iii. Coding Method or Step Deviation Method
For Ungrouped Data   For Grouped Data   • Relation Between Central moments in Terms of Non Central Moments • Moments – Ration • Sheppard’s Correction for Moments of Group Data​ Charliers Check • Symmetry
In a symmetrical distribution a deviation below the mean exactly equals the corresponding deviation above the mean. It is called symmetry. For symmetrical distribution the following relations hold.

Mean = Median = Mode
Q3 - Median = Median - Q1
u3 = m3 = 0
β1 = b1 = 0

• Skewness
Skewness is the lack of symmetry in a distribution around some central value i.e. means Median or Mode. It is the degree of asymmetry.

Mean ≠ Median ≠ Mode
Q3 - Median ≠ Median - Q1
u3  = m3 ≠ 0
β1 = b1 ≠ 0 There are two types of Skewness

1. Positive Skewness
If the frequency curve has a longer tail to right, the distribution is said to be positively skewed.

2. Negative Skewness
If the frequency curve has a longer tail to left, the distribution is said to negatively skewed.

Coefficient of Skewness (SK)

Karl Pearson’s Coefficient of Skewness Bowly’s Quartile Coefficient of Skewness Moment Coefficient of Skewness Kurtosis

Moment coefficient β2 is an important measure of kurtosis. These measures define as: The moment coefficient β2 is a pure numbers and independent of the origin and unit of measurement.

If β2 > 3 distribution is Leptokurtic
If β2 = 3 distribution is Normal or Mesokurtic
If β< 3 distribution is Platy Kurtic

Or For Normal distribution, K = 0.263

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