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7.9 Summary

• Statistics is a way of coping with the variation that exists everywhere and for stating, with confidence, how uncertain we are about our conclusions.
• Methods for summarizing essential features of data are called descriptive statistics. They include measures of central tendency and variation, as well as graphical tools for depicting data.
• Populations consist of every possible observation and are generally impossible to obtain. In practice, we always use samples of limited size to represent the population. The population and sample standard deviations are denoted σ and s, respectively. The population and sample means are denoted μ and , respectively.
• Random sampling means that every possible observation of a certain condition occurs with equal probability. Since random sampling is a central assumption in statistical analysis it is of great importance that we collect data in a way that produces random samples. This is often more difficult than it seems.
• A probability density function f(x) describes the probability of finding a random variable in an infinitesimally thin interval between the values x and x + dx. This probability is equal to f(x)dx.
• A cumulative distribution function F(x) describes the probability that a random variable is smaller than the value x. F(x) increases with x and can attain values between zero and one.
• The standard normal distribution has mean zero ...

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