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Chapter 12: Problem 6

In Exercises 1-6, find the range for each group of data items. \(3,3,3,4,5,5,5\)

Short Answer

Expert verified
The range of the given data set is 2.

Step by step solution

01

Identify the highest and lowest values

In the given data set \(3,3,3,4,5,5,5\), the highest value is 5 and the lowest value is 3.
02

Calculate the range

The range is found by subtracting the lowest value from the highest value. Therefore, the range for this data set is \(5-3 = 2\).

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Key Concepts

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

Finding Range
The range in statistics is a simple, yet important concept that measures the spread or dispersion of a data set. To find the range, you need to first understand what it represents. The range is the difference between the highest and lowest values in a data set. This difference gives us an idea about how much variation or spread there is in the data.

Finding the range can be very useful in analyzing variations in data. It helps to quickly assess how wide or narrow a data set is distributed. This is particularly helpful when you are comparing different sets of data to see which one has more variation.
Highest and Lowest Values
When calculating the range, it is crucial to correctly identify the highest and lowest values within your data set. Consider the example data set of\(3, 3, 3, 4, 5, 5, 5\).
  • Highest value: This is the largest number in the data set. In our example, the highest value is 5.
  • Lowest value: This is the smallest number in the data set. In our example, the lowest value is 3.
Clearly identifying these values is the first step in calculating the range, as it directly affects the final calculation of the range.
Calculating Range
Once you have identified the highest and lowest values in your data set, calculating the range becomes straightforward. Use the formula for range:

\(\text{Range} = \text{Highest Value} - \text{Lowest Value}\)

Applying this to our example, where the highest value is 5 and the lowest value is 3, the calculation of the range is as follows:
  • Subtract the lowest value from the highest value: \(5 - 3 = 2\).
Thus, the range of this data set is 2.

This calculation helps quantify the variance in your data, providing a quick snapshot of its total spread or dispersion.

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Most popular questions from this chapter

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