Chapter 3 Descriptive Statistics - Numerical Measures

# Chapter 3 Descriptive Statistics - Numerical Measures -...

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Chapter 3 – Descriptive Statistics: Numerical Measures - Measures that are computed for data from a sample are sample statistics , if they are computed for data from a population, they are population parameters . In statistical inference, a sample statistic is referred to as the point estimator or the corresponding population parameter Measures of Location Mean - The mean , or average value, is a measure of location for a variable - The mean provides a measure of central location for the data - The mean is denoted by x bar for a sample, and by the Greek letter μ for a population - The value of variables is denoted by a subscript; the value of the variable x for the first observation is denoted by x 1 , and the second by x 2 , etc. - The formula for the sample mean is: Xbar = Σx 1 N - The formula for computing the mean of a population remains the same, but we use different notation to indicate that we are working with the entire population (Equation 3.2) Median - The median is another measure of central location for a variable; the median is the largest value in the middle when the data are arranged in ascending order (smallest value to largest value) - An even number of observations has no single middle value (the median is the average of the values for the middle two observations) - The median is sometimes preferred over the mean because the mean is easily influenced by extremely small and large data values (in general, if a data set contains extreme values, the median is often the preferred measure of central location Mode - The mode is the value that occurs with greatest frequency - IF data contains exactly two modes, the data is bimodal ; if it contains more than two modes, the data is multimodal Percentiles - A percentile provides information about how data is spread over the interval from the smallest value to the largest value - The pth percentile divides data into two parts: 1. Approximately p percent of the observations have values less than the pth percentile 2. Approximately (100-p) percent of the observations have values greater than the pth percentile

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- Calculating the pth percentile: Step 1 – Arrange the data in ascending order (smallest value to largest value) Step 2 – Compute an index i I = (p/100)n Where p is the percentile of interest and n is the number of observations Step 3 – A. if I is not an integer, round up. The next integer greater than I denotes the
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Chapter 3 Descriptive Statistics - Numerical Measures -...

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