EXAMPLE 32 Presenting the same data set as both symmetric and left-skewed

The National Center for Education Statistics sponsors the Trends in International Mathematics and Science Study (TIMSS). Science tests were administered to eighth-grade students in countries around the world (see Table 46). Construct two different histograms: one that shows the data as almost symmetric and one that shows the data as left-skewed.

Table 2.103: TABLE 46 Science test scores
Country Score Country Score Country Score
Singapore 578 New Zealand 520 Bulgaria 479
Taiwan 571 Lithuania 519 Jordan 475
South Korea 558 Slovak Republic 517 Moldova 472
Hong Kong 556 Belgium 516 Romania 470
Japan 552 Russian Federation 514 Iran 453
Hungary 543 Latvia 513 Macedonia 449
Netherlands 536 Scotland 512 Cyprus 441
United States 527 Malaysia 510 Indonesia 420
Australia 527 Norway 494 Chile 413
Sweden 524 Italy 491 Tunisia 404
Slovenia 520 Israel 488 Philippines 377

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Solution

Figure 62 is nearly symmetric, but Figure 63 is clearly left-skewed. It is important to realize that both figures are histograms of the very same data set. Clever choices for the number of classes and the class limits can affect how a histogram presents the data. The reader must therefore beware! The histogram represents a summarization of the data set, not the data set itself. Analysts may wish to supplement the histogram with other graphical methods, such as dotplots and stem-and-leaf displays, in order to gain a better understanding of the distribution of the data.

image The One Variable Statistics and Graphs applet allows you to experiment with the class width and number of classes when constructing a histogram.

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Figure 2.62: FIGURE 62 Nearly symmetric histogram of science test scores.
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Figure 2.63: FIGURE 63 Left-skewed histogram of the same science test scores.