# Statistics

Introduction:

Statistics are used everywhere; we see statistics in use every day; statistics is used to answer important and practical questions. Statistics are useful in almost all disciplines. They are used in statistical analysis of results of an experiment, prediction of future values, growth and trend analysis, systematic presentation of data in the form of tables, diagrams and graphs.

I. Probability

A. Simple- When a coin is tossed, there are two possible outcomes: heads (H) or tails (T)

B. Stratified- In general the size of the sample in each stratum is taken in proportion to the size of the stratum. This is called proportional allocation. Suppose that in a company there are the following staff: male, full-time: 90; male, part-time: 18; female, full-time: 9; female, part-time: 63 and we are asked to take a sample of 40 staff, stratified according to the above categories.

C. Random-In a cooking gas bottling plant, thousands of cylinders are filled and dispatched to the outlets every day. Should there be an inspection from the department of weights and measures, they check by random sampling; taking 5 or 10 cylinders at random and checking the weight or the pressure of the gas in the cylinder. D. Sytematic-Suppose we have six schools with populations of 150, 180, 200, 220, 260, and 490 students respectively and we want to use student population as the basis for a PPS sample of size three.

E. Cluster- a study with relatively large square fixed area plots of 50 m x 50 m had been carried out, on which all tree positions were mapped. Because the individual plots were relatively large, there were only resources available to measure.The small sample size led to a fairly high value of the estimated.

F. Multi-Stage- Highway 155 has a length of 85 miles. Ten of its 85 one-mile segments were selected and inspected. Two of these...

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