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Chapter 8: Problem 73

Find the range for each data set. See Example 9. $$ 206,206,555,556 $$

Short Answer

Expert verified
The range is 350.

Step by step solution

01

Identify the Minimum Value

The first step is to find the smallest number in the data set. In the set \(206, 206, 555, 556\), the smallest value is \(206\).
02

Identify the Maximum Value

Next, find the largest number in the data set. In this case, the largest value is \(556\).
03

Calculate the Range

The range of a data set is calculated as the difference between the maximum and minimum values. So, subtract the minimum value from the maximum value: \(556 - 206 = 350\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Minimum Value
The concept of the minimum value in a data set refers to the smallest number among all the values. Imagine you are organizing a list of numbers. Your goal is to find which number is the lowest or least. This is crucial in data set analysis as it helps establish a starting point for understanding the spread of the data.
To find the minimum value:
  • Review all the numbers in your data set carefully.
  • Identify the smallest one by comparing each number to the others.
In our example data set of \(206, 206, 555, 556\), the minimum value is \(206\). It is important to note that even if a number appears more than once, it still qualifies as the minimum if it is the smallest value.
Locating the Maximum Value
The maximum value in a data set represents the largest number found in the given numbers. This value is crucial because it represents the high end of your data spectrum, offering insight into the upper bound of your data set.To locate the maximum value:
  • Sort through the list of numbers to find the largest one.
  • Compare each number to ensure you're identifying the greatest value.
In the data set \(206, 206, 555, 556\), the maximum value is \(556\). Finding the maximum is as straightforward as finding the minimum because you follow a similar process but focus on the highest number.
The Basics of Data Set Analysis
Data set analysis involves a variety of techniques to understand and interpret the data effectively. One of the simplest analyses is calculating the range, which gives you an idea of the spread of your data by subtracting the minimum value from the maximum value.By calculating the range:
  • Determine how much variation or spread exists between the smallest and largest values.
  • Simplify comparisons between different data sets by providing a single metric to describe the variety within.
In the example calculation, you see that by taking the maximum value (\(556\)) and subtracting the minimum value (\(206\)), you get the range, which equals \(350\). A significant component of data set analysis like this helps in making sense of your data quickly and effectively, whether for statistical calculations or more advanced data insights.

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