STATISTICAL TECHNIQUES IN SOFTWARE SIX SIGMA AND DESIGN FOR SIX SIGMA (DFSS) - Software Design for Six-Sigma: A Roadmap for Excellence - page 135

TABLE 6.5 Descriptive Statistics Summary for Data in Table 6.4 (%)

Mean 53.06

Standard error 1.01

Median 55

Mode 63

Standard deviation 10.11

Sample variance 102.24

Range 44

Minimum 22

Maximum 66

First quartile (IQ 1 ) 46

Third quartile (IQ 3 ) 62

Interquartile range 16

Count 100

Sum 5306

A typical Minitab descriptive statistics command will produce the following:

Descriptive Statistics: Usage (%)
Variable

N ∗

N Mean SE Mean StDev Minimum Q1 Median Q3

0 53 . 06 1 . 01 10 . 11 22 . 00 46 . 00 55 . 00 62 . 00

Usage(%) 100

Variable Maximum
Usage(%) 66 . 00

being chosen). Hence, random numbers typically are generated from a uniform
distribution U [ a , b ]. 4
2. Samples are drawn independently with no sequence, correlation, or auto-
correlation between consecutive observations.
3. The sample size is large enough to be representative, usually n ≥ 30.

The two main methods used in inferential statistics are parameter estimation and
hypothesis testing.

6.4.1 Parameter Estimation

In estimation, a sample is used to estimate a parameter and to construct a confidence
interval around the estimated parameter. Point estimates are used to estimate the
parameter of interest. The mean (

µ y ) and standard deviation ( σ y ) are the most common

point estimates. As discussed, the population mean ( µ y ) and standard deviation ( σ y )

are estimated using sample average ( y ) and standard deviation ( s y ), respectively.

4 The continuous uniform distribution is a family of probability distributions such that for each member of
the family, all intervals of the same length on the distribution's support are equally probable. The support
is defined by the two parameters, a and b , which are its minimum and maximum values. The distribution
is often abbreviated U [ a , b ].