subject: Standard Deviation Control Limits [print this page] Introduction to standard deviation control limits:
The mathematics has various branches like geometry, statistics, number systems, probability, algebra, etc. Statistics is one of the essential chapters in math. It concerned with the terms mean, variance, mode, standard deviation, etc. Mean is used to determine the average of a given set of values. Here, we will see about the standard deviation.. Standard deviation defines regarding the data set, or a probability distribution is the square root of its variance. Standard deviation is a data set helps us to analyze the deviation or distribution. The standard deviation shows that the data points are likely to be very close to the mean.
Formulae- Standard Deviation Control Limits:
Mean-standard deviation control limits:
It is a mathematical name in the division of statistics in which it is distinct as the total average of a set of values. It is calculated by adding all the values in a given set and then divide the total sum by a number of given values.
Formula:
The formula for mean is given as
Mean =' (x_1+x_2+.....+x_n)/n.'
Where,
'x_1+x_2+.....+x_n' . = sum of numbers
n is the number of values.
Standard deviation: standard deviation control limits:
Formula:
Standard deviation = 'sqrt((sum(x-barx)^2)/n)' . = 'sqrt((sumd^2)/n)' .
Here, d is calculated by x-'barx' .
'barx' is the mean value and x is the given values.
n is the total number of given values.
Example Problem-standand Deviation Control Limits
Example 1- standard deviation control limits:
Calculate the standard deviation for a given sequence 6,10,8,12,4
Solution:
Step 1: Calculate the mean
The given sequence is 6,10,8,12,4
Write the sequence in ascending order. Therefore, the sequence is 4,6,8,10,12
We know that Mean='(x_1+x_2+......+x_n)/n' .
Here n=5
Mean='(4+6+8+10+12)/5'
Mean='40/5'
Mean=8
Therefore, the mean value is 'barx' .=8
Step 2: Calculate the standard deviation
We know that standard deviation= 'sqrt((sumd^2)/n)' .
d = x-'barx' .
xd=x-'barx'.'d^2' =(x-'barx')'^2' .
6-24
1024
800
12416
4-416
Here we have to find 'sumd^2' .
Therefore 'sumd^2 ' = 40 , n=5
We know that standard deviation='sqrt((sumd^2)/n)' .
Standard deviation=' sqrt(40/5)' .
Standard deviation='sqrt8' .
Standard deviation=2.828
Answer: Therefore, the standard deviation for the given sequence is 2.828.
