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Statisitcs Definitions Help (page 4)

By — McGraw-Hill Professional
Updated on Apr 25, 2014

Practice 2

Draw a vertical bar graph showing all the absolute-frequency data from Table 2-5, the results of a ''weighted'' die-tossing experiment. Portray each die face on the horizontal axis. Let light gray vertical bars show the absolute frequency numbers, and let dark gray vertical bars show the cumulative absolute frequency numbers.

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Solution 2

Figure 2-6 shows such a graph. The numerical data is not listed at the tops of the bars in order to avoid excessive clutter.

Fig. 2-6. Illustration for Practice 2.

Practice 3

Draw a horizontal bar graph showing all the relative-frequency data from Table 2-6, another portrayal of the results of a ''weighted'' die-tossing experiment. Show each die face on the vertical axis. Let light gray horizontal bars show the relative frequency percentages, and dark gray horizontal bars show the cumulative relative frequency percentages.

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Solution 3

Figure 2-7 is an example of such a graph. Again, the numerical data is not listed at the ends of the bars, in the interest of neatness.

Fig. 2-7. Illustration for Practice 3.

Practice 4

Draw a point-to-point graph showing the absolute frequencies of the 10-question test described by Table 2-7. Mark the population mean, the median, and the mode with distinctive vertical lines, and label them.

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Solution 4

Figure 2-8 is an example of such a graph. Numerical data is included for the population mean, median, and mode.

Fig. 2-8. Illustration for Practice 4.

Practice 5

Calculate the variance, Var(x), for the 100 test scores tabulated in Table 2-7.

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Solution 5

Recall that the population mean, μp, as determined above, is 5.89. Table 2-9 shows the ''distances'' of each score from μp, the squares of these ''distances,'' and the products of each of these squares with the absolute frequencies (the number of papers having each score from 0 to 10). At the bottom of the table, these products are all summed. The resulting number, 643.58, is 100 times the variance. Therefore:

    • Var(x) = (1/100)(643:58)
    •            = 6:4358

It is reasonable to round this off to 6.44.

Table 2-9 "Distances" of each test score xi from the population mean μp,the squares of these "distances," the products of the squares with the absolute frequencies fi, and the sum of these products. This information is used in Solution 5.

Practice 6

Calculate the standard deviation for the 100 test scores tabulated in Table 2-7.

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Solution 6

The standard deviation, σ, is the square root of the variance. Approximating:

    • σ = [Var(x)]1/2
    •     = 6:43581/2
    •     = 2:5369

It is reasonable to round this off to 2.54.

Practice problems for these concepts can be found at:  Learning the Statistics Jargon Quiz

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