frequency distribution

Examples of frequency distribution in the following topics:

• Cumulative Frequency Distributions

  • A cumulative frequency distribution displays a running total of all the preceding frequencies in a frequency distribution.
  • A cumulative frequency distribution is the sum of the class and all classes below it in a frequency distribution.
  • Rather than displaying the frequencies from each class, a cumulative frequency distribution displays a running total of all the preceding frequencies.
  • Constructing a cumulative frequency distribution is not that much different than constructing a regular frequency distribution.
  • Create the frequency distribution table, as you would normally.

• Do It Yourself: Plotting Qualitative Frequency Distributions

  • Sometimes a relative frequency distribution is desired.
  • Bar graphs for relative frequency distributions are very similar to bar graphs for regular frequency distributions, except this time, the y-axis will be labeled with the relative frequency rather than just simply the frequency.
  • This pie chart shows the frequency distribution of a bag of Skittles.
  • This graph shows the relative frequency distribution of a bag of Skittles.
  • This graph shows the frequency distribution of a bag of Skittles.

• Relative Frequency Distributions

  • Constructing a relative frequency distribution is not that much different than from constructing a regular frequency distribution.
  • Create the frequency distribution table, as you would normally.
  • Relative frequency distributions is often displayed in histograms and in frequency polygons.
  • The only difference between a relative frequency distribution graph and a frequency distribution graph is that the vertical axis uses proportional or relative frequency rather than simple frequency.
  • Just like we use cumulative frequency distributions when discussing simple frequency distributions, we often use cumulative frequency distributions when dealing with relative frequency as well.

• Creating a Sampling Distribution

  • The figure below shows a relative frequency distribution of the means.
  • The more samples, the closer the relative frequency distribution will come to the sampling distribution shown in the above figure.
  • As the number of samples approaches infinity , the frequency distribution will approach the sampling distribution.
  • This means that you can conceive of a sampling distribution as being a frequency distribution based on a very large number of samples.
  • To be strictly correct, the sampling distribution only equals the frequency distribution exactly when there is an infinite number of samples.

• Guidelines for Plotting Frequency Distributions

  • The frequency distribution of events is the number of times each event occurred in an experiment or study.
  • In statistics, the frequency (or absolute frequency) of an event is the number of times the event occurred in an experiment or study.
  • The values of all events can be plotted to produce a frequency distribution.
  • An example of the frequency distribution of letters of the alphabet in the English language is shown in the histogram in .
  • Some theoreticians have attempted to determine an optimal number of bins, but these methods generally make strong assumptions about the shape of the distribution.

• Sampling Distributions and Statistic of a Sampling Distribution

  • You can think of a sampling distribution as a relative frequency distribution with a great many samples.
  • (See Sampling and Data for a review of relative frequency).
  • The results are in the relative frequency table shown below.
  • If you let the number of samples get very large (say, 300 million or more), the relative frequency table becomes a relative frequency distribution.

• Distributions

  • This table is called a frequency table and it describes the distribution of M&M color frequencies.
  • Not surprisingly, this kind of distribution is called a frequency distribution.
  • Often a frequency distribution is shown graphically as in Figure 1.
  • Table 3 shows a grouped frequency distribution for these 20 times.
  • Grouped frequency distributions can be portrayed graphically.

• Frequency Polygons

  • Frequency polygons are a graphical device for understanding the shapes of distributions.
  • Frequency polygons are also a good choice for displaying cumulative frequency distributions.
  • The distribution is skewed.
  • Frequency polygons are useful for comparing distributions.
  • It is also possible to plot two cumulative frequency distributions in the same graph.

• Recognizing and Using a Histogram

  • A histogram is a graphical representation of the distribution of data.
  • A histogram is a graphical representation of the distribution of data.
  • The vertical axis is labeled either frequency or relative frequency.
  • The relative frequency (or empirical probability) of an event refers to the absolute frequency normalized by the total number of events:
  • If the distribution of $x$ is continuous, then $x$ is called a continuous random variable and, therefore, has a continuous probability distribution.

• One-Way Tables (Testing Goodness of Fit)

  • This hypothesis is tested by computing the probability of obtaining frequencies as discrepant or more discrepant from a uniform distribution of frequencies as obtained in the sample.
  • We do not really "expect" the observed frequencies to match the "expected frequencies" exactly.
  • The first column in Table 3 shows the normal distribution divided into five ranges.
  • It is clear that the observed frequencies vary greatly from the expected frequencies.
  • The Chi Square distribution calculator shows that p < 0.001 for this Chi Square.