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Statistical Review

Statistical Review. MMRP-8 Indria Purwantiningrum Food Science & Technology 2013. Sub topics. The Normal Curve Mean & Median Histogram Sample vs Population concept. Mean & Median. Sample Mean =. Relationship between mean, median and mode. Mean – Mode = 3 (Mean – Median). Probability.

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Statistical Review

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  1. Statistical Review MMRP-8 Indria Purwantiningrum Food Science & Technology 2013

  2. Sub topics • The Normal Curve • Mean & Median • Histogram • Sample vs Population concept

  3. Mean & Median Sample Mean =

  4. Relationship between mean, median and mode • Mean – Mode = 3 (Mean – Median).

  5. 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

  6. 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

  7. 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.

  8. Binomial Distribution • 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. 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

  10. 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

  11. Kurva Normal

  12. Sample vs Populasi

  13. Sebaran vs Frekuensi

  14. 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.

  15. 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.

  16. Chi-Square • Contrasted with t-distribution, • Used when the standard deviations are known for the sample and for the population. These are then compared.

  17. Reference • Hubbard, Statistical Quality Control for the Food Industry, Cp. 4

  18. Thank you THANK YOU

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