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Unformatted text preview: Probability and Statistics in the Life Sciences (Spring 2010) AMS 110.02 Chapter 1&2 Lecture 1 Donghyung Lee What is Statistics? The study of methods and procedure for collecting, classifying, summarizing, and analyzing data and for making scientific inferences from such data. A set of tools or methods to obtain useful information from data. Terminologies (Variables) Variable: 1. a measurable property of a collections of units of interest 2. a characteristic of a thing that can be assigned a number or a category (Samuels and Witmer 3 rd ed.) ex) blood type (A, B, AB, O), age, height Types of Variables (1) Qualitative (Categorical) Variable: A variable with no mathematical properties 1. Nominal: a categorical variable with no agreed upon order. Ex) Color of a flower : white, blue, red, 2. Ordinal: a categorical variable with an agreed upon order. Ex) Tenderness of beef: tough, slightly tough, tender, very tender, very tender. Types of Variables (2) Quantitative Variable: A variable with mathematical properties 1. Discrete: a countable variable. Ex) age of a person (in years), # of bacteria colonies , heart rate 2. Continuous: An uncountable variable. Ex) weight, length, time Terminologies (Population and Sample) Population (the population size, N): The entire group of subjects under study. ex) the weights of all students in our class Sample (the sample size, n): The selected subset of subjects from the population under study. ex) the weights of 20 student randomly selected in our class. Terminologies (Parameter and Statistic) Parameter: A numerical value calculated using information gathered from all subjects in a population. Ex) Average of weights in Stony Brook Univ. (a population) Statistic: A numerical value calculated using information gathered from a sample. Ex) Average of weights in our class (a sample) Statistical Study Example Average weight of entire (181) students in our class Randomly select 20 students in our class and measure their weights and obtain average value. (Ex: 155 pounds) What is our population? What is our sample ? What is our statistic? Measures of Central Tendency (1) Mean (arithmetic): The sum of a set of observations divided by the number of observations. ( denoted by for population and by for a sample) x 1 N i i x N = = 1 n i i x x n = = Measures of Central Tendency (2) Median : The value that most nearly lies in the middle of the data To obtain the median, 1. arrange the data in increasing order....
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 Spring '08
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