Population Skewness, Kurtosis for grouped data calculator

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Home > Statistical Methods calculators > Population Skewness, Kurtosis for grouped data calculator

Method and examples

Method

Find Population Skewness, Kurtosis for grouped data

Type your data in either horizontal or verical format,

OR

X & Frequency Class & Frequency

Rows :

Click On Generate

Consider input table values as Class & format (

)


Class and their frequency table

Mean	Quartile
Median	Deciles
Mode	Percentiles Octile Quintile

Population Variance `(sigma^2)`	Sample Variance `(S^2)`
Population Standard deviation `(sigma)`	Sample Standard deviation `(S)`
Population Coefficient of Variation	Sample Coefficient of Variation

Population Skewness	Sample Skewness
Population Kurtosis	Sample Kurtosis

Geometric mean	Harmonic mean

Mean deviation	Quartile deviation
Decile deviation	Percentile deviation

Five number summary	Box and Whisker Plots

Mode using Grouping Method

Less than type Cumulative frequency table	More than type Cumulative frequency table

Mean, Standard deviation using Direct method or Step deviation method

Class 2 - 4 4 - 6 6 - 8 8 - 10
Frequency 3 4 2 1
Class 20 - 25 25 - 30 30 - 35 35 - 40 40 - 45 45 - 50
Frequency 110 170 80 45 40 35
Class 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80
Frequency 15 25 20 12 8 5 3
X 0 1 2 3 4
Frequency 1 5 10 6 3
X 10 11 12 13 14
Frequency 3 12 18 12 3
X 1.75 1.72 1.73 1.76 1.71 1.80 1.87 2.34
Frequency 3 2 4 5 6 2 7 1
X 0 1 2 3 4
Frequency 27 9 7 5 2
X 0 1 2 3 4
Frequency 17 9 6 5 3
Class -40 - -30 -30 - -20 -20 - -10 -10 - 0 0 - 10 10 - 20 20 - 30 30 - 40
Frequency 7 10 10 20 57 23 13 10
Class 0 - 2 2 - 4 4 - 6 6 - 8 8 - 10 10 - 12
Frequency 5 16 13 7 5 4
Class 0 - 2 2 - 4 4 - 6 6 - 8 8 - 10 10 - 12
Frequency 2 7 12 19 9 1
Class 15 - 20 20 - 25 25 - 30 30 - 35 35 - 40 40 - 45 45 - 50 50 - 55 55 - 60
Frequency 3 9 14 20 35 9 6 2 2

Decimal Place =

log(x)/ln(x) Option for Geometric mean =

SolutionHelp

Solution

Solution provided by AtoZmath.com

Population Skewness, Kurtosis for grouped data calculator

1. Calculate the mean and standard deviation for the following distribution

X	6	7	8	9	10	11	12
f	3	6	9	13	8	5	4

2. Calculate the mean and standard deviation for the following distribution

Class	50-55	45-50	40-45	35-40	30-35	35-30	20-25
f	25	30	40	45	80	110	170

Example

1. Calculate Population Skewness from the following grouped data
X Frequency
0 1
1 5
2 10
3 6
4 3

Solution:
Skewness :
Mean `bar x=(sum f x)/n`

`=55/25`

`=2.2`

`x` `(2)`	`f` `(3)`	`f*x` `(4)=(2)xx(3)`	`(x-bar x)` `(5)`	`f*(x-bar x)^2` `(6)=(3)xx(5)`	`f*(x-bar x)^3` `(7)=(5)xx(6)`
0	1	0	-2.2	4.84	-10.648
1	5	5	-1.2	7.2	-8.64
2	10	20	-0.2	0.4	-0.08
3	6	18	0.8	3.84	3.072
4	3	12	1.8	9.72	17.496
---	---	---	---	---	---
--	`n=25`	`sum f*x=55`	`--	`=26`	`=1.2`

Population Standard deviation `sigma = sqrt((sum (x - bar x)^2)/n)`

`=sqrt(26/25)`

`=sqrt(1.04)`

`=1.0198`

Population Skewness `= (sum(x - bar x)^3)/(n*S^3)`

`=1.2/(25*(1.0198)^3)`

`=1.2/(25*1.0606)`

`=0.0453`

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