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数据科学代写|经济统计代写Economic Statistics代考|ECON205 Frequency Distribution

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数据科学代写|经济统计代写Economic Statistics代考|Frequency Distribution

We begin the discussion of how tabular and graphical displays can be used to summarize categorical data with the definition of a frequency distribution.
FREQUENCY DISTRIBUTION
A frequency distribution is a tabular summary of data showing the number (frequency) of observations in each of several nonoverlapping categories or classes.

Let us use the following example to demonstrate the construction and interpretation of a frequency distribution for categorical data. Coca-Cola, Diet Coke, Dr. Pepper, Pepsi, and Sprite are five popular soft drinks. Assume that the data in Table $2.1$ show the soft drink selected in a sample of 50 soft drink purchases.

To develop a frequency distribution for these data, we count the number of times each soft drink appears in Table 2.1. Coca-Cola appears 19 times, Diet Coke appears 8 times, Dr. Pepper appears 5 times, Pepsi appears 13 times, and Sprite appears 5 times. These counts are summarized in the frequency distribution in Table 2.2.

This frequency distribution provides a summary of how the 50 soft drink purchases are distributed across the five soft drinks. This summary offers more insight than the original data shown in Table $2.1$. Viewing the frequency distribution, we see that CocaCola is the leader, Pepsi is second, Diet Coke is third, and Sprite and Dr. Pepper are tied for fourth. The frequency distribution summarizes information about the popularity of the five soft drinks.

数据科学代写|经济统计代写Economic Statistics代考|Relative Frequency and Percent Frequency Distributions

A frequency distribution shows the number (frequency) of observations in each of several nonoverlapping classes. However, we are often interested in the proportion, or percentage, of observations in each class. The relative frequency of a class equals the fraction or proportion of observations belonging to a class. For a data set with $n$ observations, the relative frequency of each class can be determined as follows:
RELATIVE FREQUENCY
$$\text { Relative frequency of a class }=\frac{\text { Frequency of the class }}{n}$$
The percent frequency of a class is the relative frequency multiplied by 100 .
A relative frequency distribution gives a tabular summary of data showing the relative frequency for each class. A percent frequency distribution summarizes the percent frequency of the data for each class. Table $2.3$ shows a relative frequency distribution and a percent frequency distribution for the soft drink data. In Table $2.3$ we see that the relative frequency for Coca-Cola is $19 / 50=.38$, the relative frequency for Diet Coke is $8 / 50=.16$, and so on. From the percent frequency distribution, we see that $38 \%$ of the purchases were Coca-Cola, $16 \%$ of the purchases were Diet Coke, and so on. We can also note that $38 \%+26 \%+16 \%=80 \%$ of the purchases were for the top three soft drinks.

数据科学代写|经济统计代写ECONOMIC STATISTICS代 考|FREQUENCY DISTRIBUTION

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数据科学代写|经济统计代写ECONOMIC STATISTICS代 考|RELATIVE FREQUENCY AND PERCENT FREQUENCY DISTRIBUTIONS

Relative frequency of a class $=\frac{\text { Frequency of the class }}{n}$

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