chapter 1-Numerical Descriptive Statistics

chapter 1-Numerical Descriptive Statistics - CHAPTER 1...

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CHAPTER 1 NUMERICAL DESCRIPTIVE STATISTICS 1. What Is Statistics? 1.1. Descriptive statistics 1.2. Inferential statistics 1.2.1. Population 1.2.2. Sample 2. Numerical Descriptive Statistics 2.1. Measures of Central Tendency 2.1.1. The Arithmetic Mean 2.1.1.1. population mean μ 2.1.1.2. sample mean x ̄ 2.1.2. The Mean as the Center of Gravity of Data Set 2.1.3. The Mean is Affected by the Outlying Values 2.1.4. Weighted Mean 2.1.5. The Mean of Binary Data 2.2. Measures of Dispersion or Data Variability 1. Statistics is a discipline which studies the collection, organization, presentation, analysis and interpretation of numerical data. There are two branches of statistics: the descriptive statistics, and the inferential statistics. 1.1.Descriptive statistics Descriptive statistics is the easy part. It deals with the collection, organization, and presentation of data. Descriptive statistics involves tables, charts, and presentation of summary characteristics of the data, which include concepts such as the mean, median or standard deviation. Descriptive statistics is encountered daily in the news media. For example, in the weather report you frequently hear about the average temperature, precipitation, pollen count, etc., in a given month of the year. Or you may read about the stock market trend, changes in the mortgage rate, the rise and fall in the crime rate, students' performance in statewide tests, and many similar reports. 1.2.Inferential statistics Inferential statistics s the complicated part of statistics. It deals with inferring or drawing conclusions about the whole ( population data) from analyzing a part of a group ( sample data). An opinion poll is an example of inferential statistics. For example, to determine the voters' preference for a given political candidate a sample of registered voters is questioned from which inferences are made about the attitudes of the population of all potential voters. The reason inferential statistics is more complicated is that it involves the theories of probability and sampling distribution, subjects unfamiliar to most students of introduction to statistics. 0 20 40 60 80 100 120 140 7.5 22.5 37.5 52.5 67.5 82.5 97.5 112.5 127.5 142.5 157.5 AV per pupil Frequency Mean < Median < Mode 122.6 < 125.7 < 127.5
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1.2.1. population In inferential statistics, the term population applies to every element, observation or data in the phenomenon or group that is the subject of the analysis. Put in another way, a population consists of all the items or individuals about which you want to draw a conclusion. 1.2.2. Sample The sample is a subset or a portion of the population selected in order to estimate, or infer about, specific characteristics of the population. For example, suppose we are interested in the average age of residents of a retirement community in Florida. Table 1.1, listing the age of every resident, represents the population that is the subject of the study. The population has 608 observations. The shaded cells in the table represent the age data for a sample of size 40 randomly selected from the population. Table 1.2 contains the sample data.
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