Question

In: Statistics and Probability

What statistics and graphs can you use to answer the following question? Is the distribution unimodal,...

What statistics and graphs can you use to answer the following question?

Is the distribution unimodal, bimodal, or multimodal?

If there is more than one mode, where are the peaks, and where are the valleys?

Explain your answers.

Solutions

Expert Solution

Unimodal Distribution in Statistics

A unimodal distribution is a distribution with one clear peak or most frequent value. The values increase at first, rising to a single peak where they then decrease. The “mode” in “unimodal” doesn’t refer to the most frequent number in a data set — it refers to the local maximum in a chart. Technically there are the same thing: one mode (one common number) will equal one peak in a graph. However, when you are looking at a graph and trying to decide if it’s a unimodal distribution or not, there’s no list of numbers to guide you.

The normal distribution is an example of a unimodal distribution; The normal curve has one local maximum (peak).

Other types of distributions in statistics that have unimodal distributions are:

  • The uniform distribution.
  • The T-distribution.
  • The chi-square distribution.
  • The Cauchy distribution.

Bimodal Distribution

In bimodal distribution, there are two peaks in the graph which generally indicates that there are two different groups taken into consideration. The bimodal distribution is a continuous distribution in which two set of outputs from two processes has been blended or mixrd together. This distribution indicates that both the processes involved in it confirm to have a normal distribution individually and have different means and standard deviations.

A distribution where there are two distinct values or bins that contain more data than the others, usually separated by a gap.

The histograms can be used to show the peaks and valleys. A normal distribution is an ideal example for unimodal distribution.

The histograms can represent distributions having two or more processes occurring in one single research which contains two or more points of central location. The bimodal distribution does necessarily have two modes or two peaks.

A histogram of a bimodal distribution can look like the following graph:

Multimodal distributions

  • A distribution where there are many values or bins that contain more data than other nearby bins, usually separated by gaps.

Multimodal distributions, where there are more than two peaks, are very rare. One example of a multimodal distribution is a trimodal distribution, which has three peaks.

if more than one mode, where are the peaks, and where are the valleys

You'll notice that the graph has two distinct humps or peaks, with a valley separating them. The prefix bi means two, so a graph with two peaks is called bimodal. Each peak is a local maximum since they represent the highest values relative to the data points immediately surrounding them. The valley between these peaks is called a local minimum.


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