QUANTIFYING VARIABILITY RELATIVE TO THE MEAN (This is a modified version of a Lo

Question

QUANTIFYING VARIABILITY RELATIVE TO THE MEAN (This is a modified version of a Los Medanos College activityl Learning Objectives . Summarize the distribution of quantitative data in context. Describe the overall pattern (shape, center, and spread) and striking deviations from the pattern. Relate measures of center and spread to the shape of the distribution. Choose appropriate measures for different context. . . Describe the effect of outliers on a set of data Exploring the notion of variability (we have not defined it yet 1) Below is a set of three distributions labeled A, B, and C. Assume the scales to be the same on each horizontal axis. a) Use your own visual sense to order this set of distributions from least amount of variability to most amount of variability b) Explain what you observed or did to order this set of distributions from least amount of variability to most amount of variability. o 8 8o 80 90 tu 11.0 12.0 Valuest1 2) Below is another set of three distributions labeled D, E, and F. Assume the scales to be the same on each horizontal axis. a) Use your own visual sense to order this set of distributions from least amount of variability to most amount of variability b) Explain what you observed or did to order this set of distributions from least amount of variability to most amount of variability. 8 9 U 11 12 Values2 37

Explanation / Answer

1.

A- least variable

B- Most variable

In A, the measurements are on center, while for Data Set B the measurements vary greatly

2.

The elementary measures of variation are range, Variance, standard deviation.

The deviation is the distance of the measurements away from the mean.The variance is the sum of the squared deviations of n measurements from their mean divided by ( n – 1).

Since range is same. Now see variance

Variance lowest in E and highest in F. Because in E most of the points are on the mean So square of distance is less but in F, not a single point is on the mean.

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