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Sturge's formula is a statistical method used to determine the optimal number of classes for a frequency distribution. This formula is particularly helpful when you have a large set of data and need to create a histogram or a frequency table.
It is expressed as:

• k = 1 + 3.322 \(\cdot \log(n)\)

Here, \(k\) represents the number of classes, and \(n\) is the total number of data points in your dataset.
The formula stems from the work of statistician Herbert Sturges, who recognized the need for a systematic way to choose the number of intervals in a histogram. By using a logarithmic function, this formula ensures that the number of classes grows at a slower rate than the data itself. This provides a manageable size for your frequency distribution, balancing detail and simplicity.

Class width is an essential component in creating categories or intervals in a frequency distribution. It defines the range of values within each class and can be calculated once you have determined the number of classes using Sturge's formula.
To find the class width, you utilize the following approach:

• Class Width \( (c) = \frac{R}{k} \)

In this equation, \(R\) is the range or the difference between the highest and lowest values in your dataset, and \(k\) is the number of classes computed earlier.
Consistency across all intervals ensures that each class width remains the same, which helps in maintaining a straightforward and effective frequency distribution.

The range of data represents the spread or dispersion of your dataset by identifying the difference between the highest and lowest values. It offers a quick glimpse into the data's variability or diversity. To compute it, you simply subtract the smallest value from the largest value:

• Range \( (R) = \text{Max Value} - \text{Min Value} \)

For example, if you have ages ranging from 20 to 53, the range would be \(53 - 20 = 33\).
This measure is foundational for calculating other statistical components like variance and standard deviation, but within the context of frequency distributions, it plays a crucial role in determining class width.

The number of classes in a frequency distribution refers to the total count of categories into which data is divided. Sturge’s formula helps in determining this number effectively based on the dataset size. With a defined number of classes:

• The dataset is divided evenly, which aids in better visual understanding when creating histograms or charts.
• It helps to avoid too many classes which might confuse the representation, or too few which might oversimplify the data.

By applying this to a dataset of 135 autoworkers' ages, Sturge’s formula suggests creating about 8 classes.
This count allows for a balanced view of data distribution, making it easier to identify patterns and trends. Always aim for a number of classes that offer a clear view without distorting the data's story.