Lecture2014Ch3Fa07 - Chapter 3 Numerically Summarizing Data...

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Chapter 3 – Numerically Summarizing Data After we have become somewhat familiar with the data through representing it graphically and observing the characteristics of the distribution, we want to describe the characteristics with numerical values called descriptive statistics. Recall from Chapter 1: Defn : A parameter is a numerical characteristic of a population. Defn : A statistic is a numerical characteristic of a sample. (Remember, a sample is a subset of a population.) We want to use the value of a statistic found from the sample data to gain knowledge about the value of the corresponding parameter, which we would be able to get directly if we had access to the entire population. Measures of Central Tendency give us information about the location of the center (in some sense) of the distribution of (numeric) data values. We will discuss four measures of central tendency: mean, median, mode, and the midrange. Defn : If we have a set of n sample data values, x 1 , x 2 , … , x n , the mean of these data values is their arithmetic average: ( 29 = = + + + = n i i n x n x x x n x 1 2 1 1 1 . If we have a set of N population data values, the mean of these values is: ( 29 = = + + + = N i i N x N x x x N 1 2 1 1 1 μ . Note : x is a statistic; μ is a parameter. Example : p. 123, Example 6 1) Go to STAT , 1:Edit. 2) Enter the data, with a suitable variable name, such as BP. 3) Choose STAT , CALC , 1:1-Var Stats . 4) Enter the variable name, and press ENTER . 5) You will see a list of numerical values for the data, including 488 . 7 = x , and 4 . 374 50 1 = = i i x . The average, or mean, birthweight for the babies was found to be 7.448 pounds. The total weight for the babies is 374.4 pounds. Properties of the Mean: 1) One computes the mean by using all of the values of the data. 2) The mean varies less than the other two measures of central tendency when samples are taken from the same population and all three measures are computed for these samples.
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3) The mean is used in computing other statistics, such as the variance. 4) The mean for the data set is unique, and not necessarily one of the data values. 5) The mean is affected by extremely high or low values and may not be the appropriate measure to use in these situations. Example: Suppose that we had made a mistake in entering the data for the first baby, entering 0.8, rather than 5.8. The computed value of the mean would be 388 . 7 = x pounds, somewhat lower than the value computed from the correct data. Sometimes, the correct raw data has extreme values. In these situations, the mean may not be the best measure of central tendency to use. In such cases, we might prefer to use the median. Defn
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This note was uploaded on 07/28/2011 for the course STA 2014 taught by Professor Staff during the Fall '10 term at University of Florida.

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Lecture2014Ch3Fa07 - Chapter 3 Numerically Summarizing Data...

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