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Math and Distributions Help

By — McGraw-Hill Professional
Updated on Oct 25, 2011

Distribution

A distribution is a description of the set of possible values that a random variable can take. This can be done by noting the absolute or relative frequency. A distribution can be illustrated in terms of a table, or in terms of a graph.

Discrete Versus Continuous

Table 7-1 shows the results of a single, hypothetical experiment in which a die is tossed 6000 times. Figure 7-3 is a vertical bar graph showing the same data as Table 7-1. Both the table and the graph are distributions that describe the behavior of the die. If the experiment is repeated, the results will differ. If a huge number of experiments is carried out, assuming the die is not “weighted,” the relative frequency of each face (number) turning up will approach 1 in 6, or approximately 16.67%.

Table 7-1 Results of a single, hypothetical experiment in which an “unweighted” die is tossed 6000 times.

Face of die

Number of times face turns up

1

  968

2

1027

3

1018

4

  996

5

1007

6

  984

A Statistics Sampler DISCRETE VERSUS CONTINUOUS

Fig. 7-3. Results of a single, hypothetical experiment in which an “unweighted” die is tossed 6000 times.

Table 7-2 Number of days on which measurable rain occurs in a specific year, in five hypothetical towns.

Town name

Number of days in year with measurable precipitation

Happyville

108

Joytown

  86

Wonderdale

198

Sunnywater

259

Rainy Glen

  18

Table 7-2 shows the number of days during the course of a 365-day year in which measurable precipitation occurs within the city limits of five different hypothetical towns. Figure 7-4 is a horizontal bar graph showing the same data as Table 7-2 . Again, both the table and the graph are distributions. If the same experiment were carried out for several years in a row, the results would differ from year to year. Over a period of many years, the relative frequencies would converge towards certain values, although long-term climate change might have effects not predictable or knowable in our lifetimes.

Both of the preceding examples involve discrete variables. When a distribution is shown for a continuous variable, a graph must be used. Figure 7-5 is a distribution that denotes the relative amount of energy available from sunlight, per day during the course of a calendar year, at a hypothetical city in the northern hemisphere.

A Statistics Sampler DISCRETE VERSUS CONTINUOUS

Fig. 7-4. Measurable precipitation during a hypothetical year, in five different imaginary towns.

A Statistics Sampler DISCRETE VERSUS CONTINUOUS

Fig. 7-5. Relative energy available from sunlight, per day, during the course of a calendar year at a hypothetical location.

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