frequency

Examples of frequency 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.
  • The second column should be labeled Frequency.

• Relative Frequency Distributions

  • To find the relative frequencies, divide each frequency by the total number of data points in the sample.
  • 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.
  • To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row.

• 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.

• Guidelines for Plotting Frequency Distributions

  • In statistics, the frequency (or absolute frequency) of an event is the number of times the event occurred in an experiment or study.
  • These frequencies are often graphically represented in histograms.
  • The relative frequency (or empirical probability) of an event refers to the absolute frequency normalized by the total number of events.
  • The height of a rectangle is also equal to the frequency density of the interval, i.e., the frequency divided by the width of the interval.
  • A histogram may also be normalized displaying relative frequencies.

• Frequency Polygons

  • Frequency polygons are also a good choice for displaying cumulative frequency distributions.
  • Draw the Y-axis to indicate the frequency of each class.
  • A frequency polygon for 642 psychology test scores shown in Figure 1 was constructed from the frequency table shown in Table 1.
  • Since the lowest test score is 46, this interval has a frequency of 0.
  • Frequency polygons are useful for comparing distributions.

• Frequency

  • Below is a frequency table listing the different data values in ascending order and their frequencies.
  • Cumulative relative frequency is the accumulation of the previous relative frequencies.
  • To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row.
  • To find the relative frequency, divide the frequency by the total number of data values.
  • To find the cumulative relative frequency, add all of the previous relative frequencies to the relative frequency for the current row.

• Creating a Sampling Distribution

  • The frequencies of these means are shown below.
  • 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.
  • After thousands of samples are taken and the mean is computed for each, a relative frequency distribution is drawn.
  • As the number of samples approaches infinity , the frequency distribution will approach the sampling distribution.

• Recognizing and Using a Histogram

  • 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.
  • The height of a rectangle in a histogram is equal to the frequency density of the interval, i.e., the frequency divided by the width of the interval.
  • A histogram may also be normalized displaying relative frequencies.

• 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.
  • Note that the expected frequencies are expected only in a theoretical sense.
  • We do not really "expect" the observed frequencies to match the "expected frequencies" exactly.
  • Letting E be the expected frequency of an outcome and O be the observed frequency of that outcome, compute
  • It is clear that the observed frequencies vary greatly from the expected frequencies.

• 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.