### Statistical Review - University of Brawijaya

```STATISTICAL REVIEW
MMRP-8
Indria Purwantiningrum
Food Science & Technology
2013
SUB TOPICS
The Normal Curve
 Mean & Median
 Histogram
 Sample vs Population concept

MEAN & MEDIAN
No
Length (mm)
1
144
2
146
3
154
4
146
Sum
590
Sample Mean =
RELATIONSHIP BETWEEN MEAN, MEDIAN
AND MODE

Mean – Mode = 3 (Mean – Median).
PROBABILITY
Express the uncertainty
 Sample & random samples (representativeness)
 Probability, p= r/n

p=probability of obtaining defective articles
 r=defective articles found
 n=number of inspected articles


Otherwise, q=(n-r)/n


Q=probability of obtaining non-defective articles
If p=0, no defectives found; p=1  all articles are
defective
TERMS
Data  observation within limit
 Samples  part of population, selected as data
 Population  the total items
 Distribution  position, arrangement, or
frequency of occurrence of data within population

TYPES OF DISTRIBUTION
Binomial
 Poisson
 Normal
 T- distribution
 F-distribution
 Exponential
 Weibull
 Chi-square
 Others—multinomial, hypergeometric, uniform,
Cauchy, gamma, beta, bivariate normal,
geometric, Pascal’s, Maxwell.

BINOMIAL DISTRIBUTION
Also called Bernoulli distribution
 The probability that an event will happen exactly
x times in n trials
 Formula (binomial theorem)

(a  b)

n
useful in sampling plans & establishing control
chart for attributes
POISSON DISTRIBUTION
Approximation to binomial distribution that is
valid when samples are large & probabilities are
small
 Useful for:

Developing defect (Nonconforming unit) control chart
 Calsulating sampling plan probabilities

NORMAL DISTRIBUTION
Variable examnied is the result of many causes
that have 50/50 chance of occuring
 Used in control chart for variables
 Although the population may not be normally
distributed  averages of groups of samples
selected generally follow this distribution types

KURVA NORMAL
SAMPLE VS POPULASI
SEBARAN VS FREKUENSI
T-DISTRIBUTION

A somewhat nonnormal curve produced when
comparing samples and population means when
the population standard deviations are unknown
and must be estimated from the samples.
F-DISTRIBUTION
 The distribution of the ratio of two estimates of
variance.
EXPONENTIAL

Logarithmic curves which describe events such
as flavor loss, shelf life, or container failure.
WEIBULL
 May take many shapes
 Based on a single formula with three variables:
shape, scale, and location.
 Used to study shelf life and product failure rates.
CHI-SQUARE
Contrasted with t-distribution,
 Used when the standard deviations are known
for the sample and for the population. These are
then compared.

REFERENCE

Hubbard, Statistical Quality Control for the Food
Industry, Cp. 4
THANK YOU
THANK YOU
```