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Quartiles and Deciles Help (page 2)

By — McGraw-Hill Professional
Updated on Sep 13, 2011

Deciles in Tabular Data

One more time, let's scrutinize the 40-question test whose results are portrayed in Table 4-1.

Percentiles

Where do we put the decile points? We break the 1000 test papers into 10 different groups with nine different boundary points according to these criteria:

  • The highest possible boundary point representing the ''worst'' 100 or fewer papers, and the 1st decile point at the top of that set.
  • The highest possible boundary point representing the ''worst'' 200 or fewer papers, and the 2nd decile point at the top of that set.
  • The highest possible boundary point representing the ''worst'' 300 or fewer papers, and the 3rd decile point at the top of that set.
  • he highest possible boundary point representing the ''worst'' 900 or fewer papers, and the 9th decile point at the top of that set.

The nomograph of Fig. 4-2B illustrates the positions of the decile points for the test results shown by Table 4-1. As is the case with quartiles, the data in the table are coincidental, because the deciles are obvious. There are clear boundaries between the ''worst'' 100 papers and the ''2nd worst,'' between the ''2nd and 3rd worst,'' between the ''3rd and 4th worst,'' and so on up. If these same 1000 students are given another 40-question test, or if this 40- question test is administered to a different group of 1000 students, it's almost certain that the locations of the decile points will be less obvious. (By now you should be able to tell that this table has been contrived to make things come out neat.)

Fig. 4-2B. At B, positions of the deciles.

Quartiles and Deciles Practice Problems

Practice 1

Table 4-2 shows a portion of results for the same 40-question test, but with slightly different results from those shown in Table 4-1, so that the 1st quartile point is not ''cleanly'' defined. Where is the 1st quartile point here?

Solution 1

Interpret the definition literally. The 1st quartile is the highest possible boundary point at the top of the set of the ''worst'' 250 or fewer papers. In Table 4-2, that corresponds to the transition between scores of 16 and 17.

Table 4-2 Table for Practice 1.

Practice 2

Table 4-3 shows a portion of results for the same 40-question test, but with slightly different results from those portrayed in Table 4-1. Here, the 6th decile point is not ''cleanly'' defined. Where is that point in this case?

Table 4-3 Table for Practice 2.

Quartiles and Deciles

Solution 2

Once again, interpret the definition literally. The 6th decile is the highest possible boundary point at the top of the set of the ''worst'' 600 or fewer papers. In Table 4-3, that corresponds to the transition between scores of 26 and 27.

Practice problems for these concepts can be found at:

Descriptive Measures Practice Test

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