1. S TATISTICAL R EVIEW MMRP-8 Indria Purwantiningrum Food Science & Technology 2013

2. S UB TOPICS The Normal Curve Mean & Median Histogram Sample vs Population concept

3. M EAN & M EDIAN NoLength (mm) 1144 2146 3154 4146 Sum590 Sample Mean =

4. R ELATIONSHIP BETWEEN MEAN, MEDIAN AND MODE Mean – Mode = 3 (Mean – Median).

5. P ROBABILITY 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

6. T ERMS 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

7. T YPES OF D ISTRIBUTION Binomial Poisson Normal T- distribution F-distribution Exponential Weibull Chi-square Others—multinomial, hypergeometric, uniform, Cauchy, gamma, beta, bivariate normal, geometric, Pascal’s, Maxwell.

8. B INOMIAL D ISTRIBUTION Also called Bernoulli distribution The probability that an event will happen exactly x times in n trials Formula (binomial theorem) useful in sampling plans & establishing control chart for attributes

9. P OISSON D ISTRIBUTION 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

10. N ORMAL D ISTRIBUTION 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

11. K URVA N ORMAL

12. S AMPLE VS P OPULASI

13. S EBARAN VS F REKUENSI

14. T -D ISTRIBUTION 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.

15. E XPONENTIAL 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.

16. C HI -S QUARE Contrasted with t-distribution, Used when the standard deviations are known for the sample and for the population. These are then compared.

17. R EFERENCE Hubbard, Statistical Quality Control for the Food Industry, Cp. 4

18. T HANK YOU