Descriptive statistics
Statistical tests
Design of Experiment
Gage RR
Problem resolution
Reliability
Control plan

# 95% interval

As we saw from the averages calculation, it is rarely possible to calculate the exact distribution average because we do not know the distribution function. It is simply possible to estimate the average with the following calculation:
Because this calculation is an approximation, you just need to know the approximation's precision. Generally, to characterize the approximation's precision we calculate the 95% interval. This interval corresponds to:
***95% interval = the interval in which there is a 95% chance that the true value of the distribution average is found inside. ***
This interval is calculated in the following way:
With:
• mu: Estimated average value of the distribution
• sigma: Estimated standard deviation value of the distribution
• n: Number of values in the series
• t: The inverse student distribution at 2.5% for n degrees of freedom. For the first approximation we can take t=2
The width of the confidence interval therefore depends on the standard deviation of the distribution of the number of values in the series. The higher the number of values the more the confidence interval will be reduced.
Example :
Let us take the following data set: .
The calculated average value is of -0.0708.
There is a 95% chance that the true average value of the sample distribution is between -0.05129 and 0.03712.

## A complete solution for Industry 4.0

8 Statistical Modules  Trial

0

1 month

APC

SPC

Control

Analysis  1 month  All feature's of Ellistat's Analysis Module.  1 user  Student / Teacher

0

1 year

Checkout

Analysis  1 year  All feature's of Ellistat's Analysis Module.  1 user  Dedicated student licence upon presenting a valud student card.  Standard

49

per user per month

Checkout

Analysis  Automatic monthly renewal  All feature's of Ellistat's Analysis Module.  Unlimited users.  