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Unformatted text preview: Ungrouped Data MATH 306 Probability and Statistics OBJECTIVES The students at the end of the lesson are expected to: • Define and Differentiate various measures of describing data • Describe a given set of data using various measures • Interpret values that arises from computation Measures of Describing Data • Measure of Central Tendency – Also known as Measure of Center, Measure of Central Location – Measure of finding the mean, median or mode of the data set • Measure of Position – Measure of finding the k th element of the distribution. Also the quantiles or fractiles of distribution • Measure of Variation – Measure of how the data is distributed abouth the mean. • Measure of Shape Measure of Central Location • Mean – A parameter used to locate the average value or that would have the same effect as all of the data • Median – The middle element of the distribution • Mode – The most frequent data in the distribution Mean • Most widely used parameter of describing a ratio data. • May be classified as – Arithmentic Mean – Geometric Mean – Harmonic Mean – Trimmed Mean – Quadratic or Root Mean Square Arithmetic Mean • The arithmetic Average of the distribution Population Mean Sample Mean for discrete data. for continuous case N x N i i ∑ = = 1 μ n x x n i i ∑ = = 1 L U xdx U L = ∫ μ Arithmetic Mean A food inspector examined a random sample of 7 cans of certain brand of peanut butter to determine the amount of foreign substance in mL. The following data were recorded: 1.8, 2.1, 1.7, 1.6, 0.9, 2.7, and 1.8. Compute the sample mean. 7 8 . 1 7 . 2 9 . 6 . 1 7 . 1 1 . 2 8 . 1 + + + + + + = x x = 1.8 mL Arithmetic Mean If a total grade of 70% must be acquired by a student in Statistics, based on the average of the 3 quizzes, what should be Mary’s score on the third quiz if she got 60 and 85 in the first two quizzes? Determine the average consumption of household of a newly installed meter where the first 10 meter readings were found as follows: 2038 56 70 84 100 115 128 142 160 Arithmetic Mean • Determine the Average voltage of a signal that follows the following waveforms: a.V = 10 sin t 0 < t < pi b.V = t 0 < t <1 c. < ≤ < < = 2 1 1 1 t t V Geometric Mean • The geometric mean is used in factors being multiplied to another quantity. Examples of which are interest and discount rates, amplification factors being used. The formula for geometric mean is given by: • What is the geometric mean between the numbers 5, 9, 25, and 80?...
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This note was uploaded on 02/17/2012 for the course ANY 191 taught by Professor Any during the Spring '12 term at Mapúa Institute of Technology.
 Spring '12
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