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Chapter 1: Problem 88

Find the mean and the range for each set of numbers. [Examples\(17-20\)] $$5,7,9,12,12$$

Short Answer

Expert verified
The mean is 9 and the range is 7.

Step by step solution

01

Identify the Numbers

Identify the set of numbers from the given data: \(5, 7, 9, 12, 12\). These are the values we will use to calculate the mean and range.
02

Calculate the Mean

To find the mean, add up all the numbers and then divide by the number of values. The sum of the numbers is \(5 + 7 + 9 + 12 + 12 = 45\). The mean is \(\frac{45}{5} = 9\).
03

Find the Maximum and Minimum

Identify the highest number (maximum) and the lowest number (minimum) in the set. The maximum number is \(12\), and the minimum number is \(5\).
04

Calculate the Range

Subtract the minimum number from the maximum number to find the range. The range is \(12 - 5 = 7\).

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Key Concepts

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

Understanding Mean Calculation
The mean of a set of numbers is often referred to as the "average." To calculate the mean, you follow a simple process:
  • First, sum all the numbers in the set. For example, if you have the numbers 5, 7, 9, 12, and 12, you add them together to get 45.
  • Next, count how many numbers there are in total. In our example, there are 5 numbers.
  • Finally, divide the total sum by the number of numbers. So, you divide 45 by 5, which results in a mean of 9.
The mean gives you a central value, which helps you understand a typical number in the set. It's especially useful because it "smooths out" the numbers to one representative value.
Exploring Range Calculation
The range is another way to describe a set of numbers, focusing on its spread. Calculating the range is very straightforward:
  • First, identify the largest number in the set, known as the maximum. In our example, the maximum is 12.
  • Next, identify the smallest number, called the minimum. Here, the minimum is 5.
  • Subtract the minimum from the maximum to find the range. Thus, 12 - 5 results in a range of 7.
The range gives you an idea of how "spread out" the numbers are. A small range indicates the numbers are close together, while a larger range shows more variability.
Number Set Analysis Made Simple
Analyzing a set of numbers is all about gaining insights into its characteristics, such as central tendency and spread.
  • The mean tells you about the average size of the numbers, which is useful when comparing different sets. Seeing that our mean is 9 implies that, on average, values cluster around this number.
  • The range offers insights into the variability. A range of 7 suggests that the numbers span across 7 units, indicating moderate variation among numbers.
Together, these calculations provide a quick snapshot of the data set and are helpful in making comparisons or understanding patterns. This understanding is crucial in diverse fields like statistics, research, and even day-to-day decision making. By knowing the mean and range, you can better interpret data and draw informed conclusions.

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Most popular questions from this chapter

Work each of the following subtraction problems. [Examples 1, 2] $$\begin{array}{r} 904 \\ -501 \\ \hline \end{array}$$

Use the distributive property to rewrite expression, then simplify. \(7(2+3)\)

Write each of the following numbers in words. $$3,040$$

Use the definition of exponents as indicating repeated multiplication to simplify each of the following expressions. [Examples \(4-12\) ] $$16^{0}$$

Round each of the numbers to the nearest ten. $$56,782$$
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