This document defines and explains key statistical concepts including measures of central tendency (mean, median, mode), measures of dispersion (range, standard deviation), and properties of distributions (skewness, symmetry). It provides examples of calculating the mean, median, mode, and standard deviation. It also describes the empirical rule and how a certain percentage of values in a normal distribution fall within 1, 2, or 3 standard deviations of the mean.
10. Skewness Mode = Mean = Median SYMMETRIC Figure 2-13 (b)
11. Skewness Mode = Mean = Median SKEWED LEFT (negatively ) SYMMETRIC Mean Mode Median Figure 2-13 (b) Figure 2-13 (a)
12. Skewness Mode = Mean = Median SKEWED LEFT (negatively ) SYMMETRIC Mean Mode Median SKEWED RIGHT (positively) Mean Mode Median Figure 2-13 (b) Figure 2-13 (a) Figure 2-13 (c)
20. Estimation of Standard Deviation Range Rule of Thumb x - 2 s x x + 2 s Range 4 s or (minimum usual value) (maximum usual value)
21. Estimation of Standard Deviation Range Rule of Thumb x - 2 s x x + 2 s Range 4 s or (minimum usual value) (maximum usual value) Range 4 s
22. Estimation of Standard Deviation Range Rule of Thumb x - 2 s x x + 2 s Range 4 s or (minimum usual value) (maximum usual value) Range 4 s = highest value - lowest value 4
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26. x The Empirical Rule (applies to bell-shaped distributions ) FIGURE 2-15
27. x - s x x + s 68% within 1 standard deviation 34% 34% The Empirical Rule (applies to bell-shaped distributions ) FIGURE 2-15
28. x - 2s x - s x x + 2s x + s 68% within 1 standard deviation 34% 34% 95% within 2 standard deviations The Empirical Rule (applies to bell-shaped distributions ) 13.5% 13.5% FIGURE 2-15
29. x - 3s x - 2s x - s x x + 2s x + 3s x + s 68% within 1 standard deviation 34% 34% 95% within 2 standard deviations 99.7% of data are within 3 standard deviations of the mean The Empirical Rule (applies to bell-shaped distributions ) 0.1% 2.4% 2.4% 13.5% 13.5% FIGURE 2-15 0.1%
Hinweis der Redaktion
page 58 of text Name the two values if the set is bimodal
Data skewed to the left is said to be ‘negatively skewed’ with the mean and median to the left of the mode. Data skewed to the right is said to be ‘positively skewed’ with the mean and media to the right of the mode.
Data not ‘lopsided’.
Data lopsided to left (or slants down to the left - definition of skew is ‘slanting’)
Data lopsided to the right (or slants down to the right)
Reminder: range is the highest score minus the lowest score
Reminder: range is the highest score minus the lowest score
Reminder: range is the highest score minus the lowest score
These ideas will be used repeatedly throughout the course.
page 79 of text
Some student have difficulty understand the idea of ‘within one standard deviation of the mean’. Emphasize that this means the interval from one standard deviation below the mean to one standard deviation above the mean.
These percentages will be verified by the concepts learned in Chapter 5. Emphasize the Empirical Rule is appropriate for data that is in a BELL-SHAPED distribution.
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