Download Pointers for Section 3.3

Pointers for Section 3.3 This section covers how to approximate the mean and standard deviation for group data, or data that has been summarized in a frequency distribution. DO NOT use this process if you have the actual, raw data. Grouped Data v. Raw Data Grouped Data is data that has been summarized in a frequency distribution table or a histogram. Raw Data is the actual, real data values For example: {2,2,3,3,4,4,4,4,5} is an actual, raw data set. I can see the exact value for each piece of data. This same data set may be grouped together in the following frequency distribution: Class Limits Frequency 2.00 – 3.99 4 4.00 – 5.99 5 If I only had access to the frequency distribution pictured above, I would understand that I had 4 values between 2.00 – 3.99, but I would not know exactly what those values are unless I have access to the raw data. Approximating the Mean of Grouped Data If your do not have access to the actual, raw data, the best you can do is approximate the mean of frequency distribution table. Recall that the mean is one of the ways that we measure the “central tendency” of a data set. If you are approximating the mean of a population, use the symbol µ. (pronounced: “mu” or “mew”) If you are approximating the mean of a sample, use the symbol 𝑥 -­‐ . (pronounced: “x-­‐bar”) StatCrunch – How to calculate the Mean of Grouped Data (Frequency Distribution Table) •
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Enter summarized data into StatCrunch. Click Stat button >Summary Stats> Grouped / Binned Data Choose the column that contains the classes under the “Bins in” drop-­‐down menu. Choose the column that contains the frequencies in the “Counts in” drop-­‐down menu. Under the Midpoints section: • Choose “Limits” if your class limits are discrete (i.e. single values) • Choose “Consecutive lower limits” if your class limits are continuous (i.e. range of values) For Statistics, make sure that “Mean” is selected. Click on Compute! Developed by Sharleen McCarroll in conjunction with the textbook Interactive Statistics: Informed Decisions Using Data, by Michael Sullivan III & George Woodbury, 2016. Weighted Mean A weighted mean is used when different data values have different “weights” toward the total. For example, your college grade point average, or gpa, is “weighted” by the units (or hours) of each course. So, a four-­‐unit Statistics course will impact your gpa more than a one-­‐unit P.E. course. In a four-­‐unit course, you are expected to do more work throughout the semester, thus it will count more toward your overall gpa than a one-­‐unit class. In a weighted mean, you CANNOT simply add the values together and divide by the total number of items. You MUST take into account how much each time “counts” or “weighs” toward the total. StatCrunch – How to calculate a Weighted Mean •
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Enter the value of the variable in the first column and the weights in the second column. Click Stat button >Summary Stats> Grouped / Binned Data Choose the column that contains the values under the “Bins in” drop-­‐down menu. Choose the column that contains the weights in the “Counts in” drop-­‐down menu. Choose “Limits” button for defining the midpoints. For Statistics, make sure that “Mean” is selected. Click on Compute! Approximating the Standard Deviation of Grouped Data If you do not have access to the actual, raw data, the best you can do is approximate the standard deviation of frequency distribution table. Recall that the standard deviation is one of the ways that we measure the “spread” of a data set. Population v. Sample Standard Deviation If you are approximating the standard deviation of a population, use the symbol 𝜎 . (pronounced: “sigma”) If you are approximating the standard deviation of a sample, use the symbol 𝑠 -­‐ . Remember: There is a difference in formula, so it is critical for you to know whether your data comes from a sample or a population. StatCrunch – How to calculate the Standard Deviation of Grouped Data (Frequency Distribution Table) •
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Enter summarized data into StatCrunch. Click Stat button >Summary Stats> Grouped / Binned Data Choose the column that contains the classes under the “Bins in” drop-­‐down menu. Choose the column that contains the frequencies in the “Counts in” drop-­‐down menu. Under the Midpoints section: • Choose “Limits” if your class limits are discrete (i.e. single values) • Choose “Consecutive lower limits” if your class limits are continuous (i.e. range of values) For Statistics, • Choose “Std. Dev.” For SAMPLE Standard Deviation • Choose “Unadj. Std. Dev.” For POPULATION Standard Deviation Click on Compute!