#### Transcript 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