Mean deviation, Coefficient of Mean deviation for grouped data calculator

We use cookies to improve your experience on our site and to show you relevant advertising. By browsing this website, you agree to our use of cookies. Learn more

AtoZmath.com

Support us

(New) All problem can be solved using search box

~~I want to sell my website www.AtoZmath.com with complete code~~

College Algebra

Feedback

Matrix & Vector

Numerical Methods

Statistical Methods

Operation Research

Home > Statistical Methods calculators > Mean deviation, Coefficient of Mean deviation for grouped data calculator

Method and examples

Method

Mean deviation, Coefficient of Mean deviation for grouped data calculator

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, Coefficient of M.D.	Quartile deviation, Coefficient of Q.D., Interquartile range
Decile deviation, Coefficient of D.D., Interdecile range	Percentile deviation, Coefficient of P.D., Interpercentile range

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

Mean deviation, Coefficient of Mean deviation 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 Mean deviation, Coefficient of M.D. from the following grouped data
X Frequency
0 1
1 5
2 10
3 6
4 3

Solution:
Mean deviation :

`x` `(1)`	`f` `(2)`	`f*x` `(3)=(2)xx(1)`	`\|x-bar x\|=\|x-2.2\|` `(4)`	`f*\|x-bar x\|` `(5)=(2)xx(4)`
0	1	0	2.2	2.2
1	5	5	1.2	6
2	10	20	0.2	2
3	6	18	0.8	4.8
4	3	12	1.8	5.4
---	---	---	---	---
--	`n=25`	*`sum fx=55`**	--	*`sum f\|x-bar x\|=20.4`**

Mean `bar x=(sum f x)/n`

`=55/25`

`=2.2`

Mean deviation of Mean
`delta bar x = (sum f*|x - bar x|)/n`

`delta bar x = 20.4/25`

`delta bar x = 0.816`

Coefficient of Mean deviation `=(delta bar x)/(bar x)`

`=0.816/2.2`

`=0.3709`

Share this solution or page with your friends.

College Algebra

Feedback

Copyright © 2025. All rights reserved. Terms, Privacy

.