# 数据科学代写|经济统计代写Economic Statistics代考|ECON101 Width of the Classes

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## 数据科学代写|经济统计代写Economic Statistics代考|Width of the Classes

Width of the Classes The second step in constructing a frequency distribution for quantitative data is to choose a width for the classes. As a general guideline, we recommend that the width be the same for each class. Thus the choices of the number of classes and the width of classes are not independent decisions. A larger number of classes means a smaller class width, and vice versa. To determine an approximate class width, we begin by identifying the largest and smallest data values. Then, with the desired number of classes specified, we can use the following expression to determine the approximate class width.
Approximate class width $=\frac{\text { Largest data value }-\text { Smallest data value }}{\text { Number of classes }}$
The approximate class width given by equation (2.2) can be rounded to a more convenient value based on the preference of the person developing the frequency distribution. For example, an approximate class width of $9.28$ might be rounded to 10 simply because 10 is a more convenient class width to use in presenting a frequency distribution.

For the data involving the year-end audit times, the largest data value is 33 and the smallest data value is 12 . Because we decided to summarize the data with five classes, using equation (2.2) provides an approximate class width of $(33-12) / 5=4.2$. We therefore decided to round up and use a class width of five days in the frequency distribution.
In practice, the number of classes and the appropriate class width are determined by trial and error. Once a possible number of classes is chosen, equation (2.2) is used to find the approximate class width. The process can be repeated for a different number of classes. Ultimately, the analyst uses judgment to determine the combination of the number of classes and class width that provides the best frequency distribution for summarizing the data.
For the audit time data in Table $2.4$, after deciding to use five classes, each with a width of five days, the next task is to specify the class limits for each of the classes.

## 数据科学代写|经济统计代写Economic Statistics代考|Class limits

Class limits Class limits must be chosen so that each data item belongs to one and only one class. The lower class limit identifies the smallest possible data value assigned to the class. The upper class limit identifies the largest possible data value assigned to the class. In developing frequency distributions for categorical data, we did not need to specify class limits because each data item naturally fell into a separate class. But with quantitative data, such as the audit times in Table $2.4$, class limits are necessary to determine where each data value belongs.

Using the audit time data in Table 2.4, we selected 10 days as the lower class limit and 14 days as the upper class limit for the first class. This class is denoted 10-14 in Table $2.5$. The smallest data value, 12, is included in the 10-14 class. We then selected 15 days as the lower class limit and 19 days as the upper class limit of the next class. We continued defining the lower and upper class limits to obtain a total of five classes: 10-14, 15-19, 20-24, $25-29$, and 30-34. The largest data value, 33, is included in the 30-34 class. The difference between the lower class limits of adjacent classes is the class width. Using the first two lower class limits of 10 and 15 , we see that the class width is $15-10=5$.
With the number of classes, class width, and class limits determined, a frequency distribution can be obtained by counting the number of data values belonging to each class. For example, the data in Table $2.4$ show that four values-12, 14,14 , and 13 -belong to the $10-14$ class. Thus, the frequency for the $10-14$ class is 4 . Continuing this counting process for the 15-19,20-24, 25-29, and 30-34 classes provides the frequency distribution in Table 2.5. Using this frequency distribution, we can observe the following:

1. The most frequently occurring audit times are in the class of 15-19 days. Eight of the 20 audit times belong to this class.
2. Only one audit required 30 or more days.
Other conclusions are possible, depending on the interests of the person viewing the frequency distribution. The value of a frequency distribution is that it provides insights about the data that are not easily obtained by viewing the data in their original unorganized form.

## 数据科学代写|经济统计代写ECONOMIC STATISTICS代 考|CLASS LIMITS

1. 最常出现的审核时间为 15-19天。20个审计时间中有 8 个属于此夈。
2. 只有一项审核需要 30 天或更长时间。
其他结论是可能的，这取决于音看频率分布的人的兴趣。频率分布的价值在于它提供了有关数据的洞崇力，而这些洞腙力是通过以原始无组织形式亘看数据 不容易获得的。

## Matlab代写

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