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Central Tendency and Variability Chapter 4

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Central Tendency >Mean: arithmetic average Add up all scores, divide by number of scores >Median: middle score >Mode: most common score

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Calculating the Mean >Add up all scores >Divide by number of scores

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Calculating the Median >Line up the scores in ascending order >Find the middle number For an odd number of scores, just find the middle value. For an even number of scores, divide number of scores by two. Take the average of the scores around this position.

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Calculating the Mode >Line up the scores in ascending order. >Find the most frequent score. >That’s the Mode!

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>Do measures of central tendency capture the following slide adequately?

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Figure 4-4: Bipolar Disorder and the Modal Mood

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>An early lesson in lying with statistics Which central tendency is “best”: mean, median, or mode? Outliers and the Mean

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Figure 4-6: The Mean without the Outlier

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Which Measure of Central Tendency is the Best? >The mean is most commonly used – best for symmetric distributions >The median is best for a skewed distribution or one with outlier(s), >The mode is used in 3 cases: One particular score dominates a distribution Distribution is bimodal or multimodal Data are nominal

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Measures of Variability >Range From the lowest to the highest score >Variance Average square deviation from the mean >Standard deviation Variation from the sample mean

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Calculating the Range >Determine the highest score >Determine the lowest score >Subtract the lowest score from the highest score

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>Subtract the mean from each score >Square every deviation from the mean >Sum the squared deviations >Divide the sum of squares by N Calculating the Variance

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>Typical amount the scores vary or deviate from the sample mean This is the square root of variance Calculating the Standard Deviation

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Practice Problem >Age of Classmates? Calculate the mean, median, mode, standard deviation, and the variance for the age of the members of your class.

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Interquartile Range >Measure of the distance between the 1 st and 3 rd quartiles. >1 st quartile: 25th percentile of a data set >The median marks the 50th percentile of a data set. >3 rd quartile: marks the 75 th percentile of a data set

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Calculating the Interquartile Range Countries’ top finishes in the World Cup omitting countries with a score of 0 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 4, 6, 8, 10

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