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Distributions Help (page 2)

By — McGraw-Hill Professional
Updated on Aug 26, 2011

Grouped frequency distribution

If we want to be more detailed, we can tabulate the frequency for each die face 1 through 6 separately for each die. A hypothetical product of this effort, called a grouped frequency distribution, is shown in Table 2-4.

Distributions

The results are grouped according to manufacturer and die color. From this distribution, it is apparent that some of the die are heavily ''weighted.'' Only the green die, manufactured by Corp. D, seems to lack any bias. If you are astute, you will notice (or at least strongly suspect) that the green die here is the same die, with results gathered from the same experiment, as is portrayed in Table 2-1 and Fig. 2-3.

Distributions

Distributions

Distributions Practice Problems

Practice 1

Suppose you add up all the numbers in each column of Table 2-4. What should you expect, and why? What should you expect if the experiment is repeated many times?

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Solution 1

Each column should add up to 6000. This is the number of times each die (red, orange, yellow, green, or blue) is tossed in the experiment. If the sum of the numbers in any of the columns is not equal to 6000, then the experiment was done in a faulty way, or else there is an error in the compilation of the table. If the experiment is repeated many times, the sums of the numbers in each column should always be 6000.

Practice 2

Suppose you add up all the numbers in each row of Table 2-4. What should you expect, and why? What should you expect if the experiment is repeated many times?

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Solution 2

The sums of the numbers in the rows will vary, depending on the bias of the set of die considered as a whole. If, taken all together, the die show any bias, and if the experiment is repeated many times, the sums of the numbers should be consistently lower for some rows than for other rows.

Practice 3

Each small rectangle in a table, representing the intersection of one row with one column, is called a cell of the table. What do the individual numbers in the cells of Table 2-4 represent?

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Solution 3

The individual numbers are absolute frequencies. They represent the actual number of times a particular face of a particular die came up during the course of the experiment.

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

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