1. What’s statistics The term of statistics is commonly used in two senses. In the first sense, we use the term statistics in our day-to-day communication when we refer to collections of numbers or facts. In the second sense, we define statistics as a scientific subject that provides the techniques of collecting, organizing, summarizing analyzing, and interpreting information in order to draw conclusions (as input to make appropriate decisions). 2. the process of Statistics (4 processes in the consecutive order) (1) Identify the research objective. Collect the information needed to answer the questions posed in (1). Organize and summarize the information(descriptive &
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Math 10041 Elementary Statistics and Probability
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statistics)
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Draw conclusions from the information(Inferential Statistics). 3. Distinguish qualitative(or categorical) variables and quantitative variables 4. what’s the difference between variables and data,what’s t he difference between continuous variable( or data) and discrete variable(or data) 5. Population. A population is a collection of all conceivable individuals, elements, numbers or entities which possess a characteristic of interest. A portion of a population selected for study is called a sample. The population from which a sample is selected is called a sampled population and the population being studied is called the target population. Every effort is made to ensure the sampled population is the &
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Math 10041 Elementary Statistics and Probability
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same as the target population. Conclusions about the population are valid only if the sample selected is a representative sample, that is, the sample possesses all characteristics of the population that is under investigation.(The techniques of Random Sample) 6. what’s the difference between population and sample 7. what’s simple random sampling, how to obtain a simple random sample
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Math 10041 Elementary Statistics and Probability
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Chapter 2
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Math 10041 Elementary Statistics and Probability
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Chapter 2 Organizing and summarizing data
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Understand that we take different approaches to organize and summarize the data for different types of variables. I Qualitative Data • know how to construct frequency and relative frequency distribution table from your qualitative data(i.e., the raw data). • Construct bar graphs/Pareto charts/side-by-side bar graphs • Pie chart II Quantitative Data • know how to construct frequency and relative frequency distribution table from your quantitative data(i.e., the raw data). &
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Math 10041 Elementary Statistics and Probability
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• Construct Histograms for discrete or continuous data • How to organize continuous data into a frequency and relative frequency table • Construct Stem-and-Leaf Plot • Time series plots of time series data.
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Math 10041 Elementary Statistics and Probability
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Statistical Data
Qualitative
Nominal
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Ordinal
Quantitative
interval
Ratio
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Math 10041 Elementary Statistics and Probability
Review Chapter 1-3
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Statistical Data
Qualitative Nominal
Quantitative
Ordinal
interval
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Ratio
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Math 10041 Elementary Statistics and Probability
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Misleading Graphs
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Math 10041 Elementary Statistics and Probability
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Chapter 3
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Math 10041 Elementary Statistics and Probability
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Chapter 3 Numerically Summarizing Data
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What’s the difference between a parameter and a statistic. 1. A Parameter is a descriptive measure of a population. 2. A statistic is a descriptive measure of a sample. mean–mathematical expectation : average : arithmetic average : Example: a sample of size 2: 4 with probability 1/4 and 8 with probability of 3/4 average: 1/2 ∗ (4 + 8) = 6 mean:4 ∗ 0.25 + 8 ∗ 0.75 = 7. if all individuals have the same probability (or you assume so), then mean is the same as average. Strictly speaking, mean is a statistical language, but average is more colloquial. &
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Math 10041 Elementary Statistics and Probability
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We have lot of different means–arithmetic mean, geometric mean,weighted mean... 1. the arithmetic Mean from grouped data(fi s are from the frequency distribution) First calculate the class midpoint Lower class Limit+Upper Class Limit Class midpoint = . 2 and then
P xi fi x1 f1 + · · · xn fn P = µ= fi f1 + · · · fn
fi : the frequency of the ith class. xi : the midpoint of the ith class. n: the number of classes 2. Weighted Mean
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Math 10041 Elementary Statistics and Probability
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Measure of central tendency and dispersion
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I Central Tendency 1. distinguish between parameter and statistic 2. the approaches to measure the central tendency(of a population or a sample) and the circumstance to use them • arithmetic mean • median • Mode 3. the approaches to measure the dispersion of a population or sample. • Range • Variance(or Standard Deviations) 4. the approaches to measure the central tendency of grouped &
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Math 10041 Elementary Statistics and Probability
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data 5. the approaches to measure the dispersion of grouped data 6. the approaches to measure the central tendency of weighted data 7. the approaches to measure the dispersion of weighted data
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Math 10041 Elementary Statistics and Probability
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Measure the position(or location )How to describe the relative position of a certain data value within the entire data set. 1. How to measure the location of a observation in a data set • Z-score • percentiles: How to determine the k-th percentile • How to find the percentile for a given data value • How to find the quartile os a data set • How to check outliers &
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Math 10041 Elementary Statistics and Probability
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the Empirical Rule • What’s the 68% interval • What’s the 95% interval • What’s the 99.7% interval
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Math 10041 Elementary Statistics and Probability
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The Shape of A Distribution • If the Histogram, or Bar graph, or Box-plot, you need to recognize the shape of the distribution • Give the relationship between the arithmetic mean and the median of a data set, recognize the shape of the distribution
