Statistical Sciences 1023A/B Chapter 7: Chapter 7

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Statistical Sciences
Course Code
Statistical Sciences 1023A/B
Lori Murray

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Chapter 7 Summarizing and Displaying Measurement Data Summarizing and Displaying Measurement Data Measuring Center: The Mean (average) To calculate the mean, simply add together all the values of the observations, then divide by the total number of observations. Summarizing and Displaying Measurement Data Measuring Center: The Median (the middle same amount of numbers above and below the number designated as the median) The median, M, is the midpoint of a distribution, the number such that half of the observations are smaller and the other half are larger. To find the median of a distribution: 1. Arrange all observations from smallest to largest. 2. If the number of observations n is odd, the median M is the center observation in the ordered list. If the number of observations n is even, the median M is the average of the two center observations in the ordered list. 3. You can always locate the median in the ordered list of observations by counting up (n + 1)2 observations from the start of the list. Terminology Mean: numerical average Median: halfway between the highest and lowest values Mode: most common occurring value Outliers: values far removed from the rest of the data Variability: How spread out are the values? Range: The amount between the lowest and highest numbers Shape: Are most values clumped in the middle with values tailing off at each end? Are there two distinct groupings? Reasons for Outliers 1) The outlier is a legitimate data value and represents natural variation in responses. In that case, the outlier should be retained and included in data summaries. 2) A mistake was made when recording the measurement or a question was misunderstood. In that case, if the correct value can be found, replace the outlier. Otherwise, delete it from the dataset before computing numerical summaries (but always report doing so.)
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