05/01/2023Departm

ent of Textile Engineering, MUET Jam

shoro

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STATISTICAL METHODASSIGNMENT ON: MEAN & STANDARD DEVIATION

Submitted to: Sir Asghar Sangah

Submitted by: Ghulam Mustafa GhoriRoll# 13TE89

05/01/2023

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Department of Textile Engineering, M

UET Jam

shoro

THE MEAN DEVIATION:- The mean deviation of a set of data is

defined as the arithmetic mean of the deviations measured either from the mean or from the median, all deviations are being counted as positive.

M.D= For sample data

M.D= For Population Data

05/01/2023

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Department of Textile Engineering, M

UET Jam

shoro Mean Deviation is an absolute measure of

dispersion. It’s relative measure is known as the co-efficient of mean deviation, is obtained by dividing the mean deviation by the average used in the calculation of deviation.

Co-efficient of M.D= or

Example#01: Calculate the M.D and it’s Co-efficient from given data

29,35,38,40,55,60,65,70

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Department of Textile Engineering, M

UET Jam

shoro

29 -20 2035 -14 1438 -11 11 40 -9 955 6 660 11 1165 16 1670 21 21

∑xi=392 ∑ =108

05/01/2023

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Department of Textile Engineering, M

UET Jam

shoro putting the values M.D=

M.D= 13.5 Now co-efficient of Mean Deviation

Coefficient of M.D= =

Co-efficient of M.D= 0.27

05/01/2023

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Department of Textile Engineering, M

UET Jam

shoroThe Variance and Standard Deviation:- The variance is the set of

observations is defined as the mean of the deviations of all the observation from their mean .When it is calculated from the entire population, the variance is called population variance. If instead, the data from sample are used to calculate the variance, it is referred to as the sample variance. The symbolic definition for variance is

= , For population data , For sample data

=

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Department of Textile Engineering, M

UET Jam

shoroStandard Deviation:- The positive square root

of the variance is called standard deviation . Symbolically

,For population data

, for sample data

The standard deviation is expressed in the same unit as the observation themselves and is measure of the average spread around the mean.

=

=

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Department of Textile Engineering, M

UET Jam

shoroExample:- A population of N=10 has the observation

7,8,10,13,14,19,20,25,26 and 28. Find it’s variance and standard deviation .

Solution:- 7 -10 100 49 8 -9 81 64 10 -7 49 100 13 -4 16 169 14 -3 9 196 19 2 4 361 20 3 9 400 25 8 64 625 26 9 81 676 28 11 121 784 174 0

534 3424

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Department of Textile Engineering, M

UET Jam

shoroNow

=

= 17Therefore

= = =53.4 Hence the Variance is 53.4

05/01/2023

10

Department of Textile Engineering, M

UET Jam

shoroAnd now we find standard deviation,

= or

=

=

= 7.31 Answer