relative frequency distribution

Examples of relative frequency distribution in the following topics:

• 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 relative frequencies are equal to the frequencies divided by nine because there are nine possible outcomes.
  • The figure below shows a relative frequency distribution of the means.
  • This distribution is also a probability distribution since the $y$-axis is the probability of obtaining a given mean from a sample of two balls in addition to being the relative frequency.
  • After thousands of samples are taken and the mean is computed for each, a relative frequency distribution is drawn.
  • The more samples, the closer the relative frequency distribution will come to the sampling distribution shown in the above figure.

• 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.

• Do It Yourself: Plotting Qualitative Frequency Distributions

  • Sometimes a relative frequency distribution is desired.
  • If this is the case, simply add a third column in the table called Relative Frequency.
  • 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.
  • Since a circle has 360 degrees, this is found out by multiplying the relative frequencies by 360.
  • This graph shows the relative frequency distribution of a bag of Skittles.

• Introduction to Sampling Distributions

  • The relative frequencies are equal to the frequencies divided by nine because there are nine possible outcomes.
  • Figure 2 shows a relative frequency distribution of the means based on Table 2.
  • After thousands of samples are taken and the mean computed for each, a relative frequency distribution is drawn.
  • The more samples, the closer the relative frequency distribution will come to the sampling distribution shown in Figure 2.
  • As the number of samples approaches infinity, the relative frequency distribution will approach the sampling distribution.

• Continuous Sampling Distributions

  • This distribution was discrete, since there were a finite number of possible observations.
  • Now we will consider sampling distributions when the population distribution is continuous.
  • Therefore, it is more convenient to use our second conceptualization of sampling distributions, which conceives of sampling distributions in terms of relative frequency distributions-- specifically, the relative frequency distribution that would occur if samples of two balls were repeatedly taken and the mean of each sample computed.
  • A probability density function, or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value.
  • Boxplot and probability density function of a normal distribution $N(0, 2)$.

• Guidelines for Plotting Frequency Distributions

  • The frequency distribution of events is the number of times each event occurred in an experiment or study.
  • The relative frequency (or empirical probability) of an event refers to the absolute frequency normalized by the total number of events.
  • 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 .
  • A histogram may also be normalized displaying relative frequencies.

• Recognizing and Using a Histogram

  • 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:
  • Put more simply, the relative frequency is equal to the frequency for an observed value of the data divided by the total number of data values in the sample.
  • A histogram may also be normalized displaying relative frequencies.

• 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.

• 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.
  • Grouped frequency distributions can be portrayed graphically.
  • The upper distribution has relatively more scores in its tails; its shape is called leptokurtic.
  • The lower distribution has relatively fewer scores in its tails; its shape is called platykurtic.