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Chapter 12: Problem 86

Give an example of a phenomenon that is not normally distributed and explain why.

Short Answer

Expert verified
The wealth distribution of a country is an example of a non-normally distributed phenomenon. This is because wealth is often highly concentrated, resulting in a positively skewed distribution, which does not fit the 'bell curve' of a normal distribution. Extreme wealth values can lead to a high level of kurtosis - more frequent extreme values than expected in a normal distribution.

Step by step solution

01

Identify a Non-Normally Distributed Phenomenon

The wealth distribution of a country is an example of a phenomenon that is not normally distributed. In many countries, wealth distribution is skewed, often in favor of a small percentage of the population who hold a disproportionately large amount of the wealth.
02

Identify Characteristics of Non-Normal Distribution

In an ideal normal or Gaussian distribution, events are equally likely to occur on either side of the average, resulting in a symmetric, bell-shaped curve. However, in the distribution of wealth in many countries, there is a high level of skewness, with wealth concentrated among a small percentage of the population. This creates a positively skewed distribution. In addition, due to extreme values, the data may exhibit high kurtosis, meaning there are fat tails and thus, more frequent extreme values than expected in a normal distribution.
03

Validate Your Selection

This distribution is a common characteristic of wealth distribution globally, characterized by high amounts of wealth held by a small proportion of the population. Therefore, the wealth distribution of a country is an excellent example of a non-normally distributed phenomenon.

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Most popular questions from this chapter

A group of data items and their mean are given.a. Find the deviation from the mean for each of the data items.b. Find the sum of the deviations in part (a). \(29,38,48,49,53,77 ;\) Mean \(=49\)

A set of data items is normally distributed with a mean of 400 and a standard deviation of 50. Find the data item in this distribution that corresponds to the given z-score. \(z=3\)

Give an example of a set of six examination grades (from 0 to 100 ) with each of the following characteristics: a. The mean and the median have the same value, but the mode has a different value. b. The mean and the mode have the same value, but the median has a different value. c. The mean is greater than the median. d. The mode is greater than the mean. e. The mean, median, and mode have the same value. f. The mean and mode have values of 72 .

A college professor had students keep a diary of their social interactions for a week. Excluding family and work situations, the number of social interactions of ten minutes or longer over the week is shown in the following grouped frequency distribution. Use this information to solve.$$ \begin{array}{|c|c|} \hline \begin{array}{c} \text { Number of } \\ \text { Social Interactions } \end{array} & \text { Frequency } \\ \hline 0-4 & 12 \\ \hline 5-9 & 16 \\ \hline 10-14 & 16 \\ \hline 15-19 & 16 \\ \hline 20-24 & 10 \\ \hline 25-29 & 11 \\ \hline 30-34 & 4 \\ \hline 35-39 & 3 \\ \hline 40-44 & 3 \\ \hline 45-49 & 3 \\ \hline \end{array} $$ Among the classes with the greatest frequency, which class has the least number of social interactions?

If your weight is in the third quartile, what does this mean?
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