Problem 76 Evaluate the expression. $$\fr... [FREE SOLUTION]

Chapter 6: Problem 76

Evaluate the expression. $$\frac{37+65+89+72+82}{5}$$

Short Answer

Expert verified

The solution is 69, which is the average of the provided numbers.

Step by step solution

Sum the Values

First add all the values together that we're taking the average of. In this case, it is 37, 65, 89, 72, and 82. The result is $37+65+89+72+82 = 345$.

Divide by the Quantity

Next, divide the sum that was calculated in step 1 by the quantity of numbers we're averaging. In this case, the denominator is 5 as we have 5 numbers, so the calculation is $345 \div 5 = 69$.

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Key Concepts

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

Addition

Addition is the process of combining two or more numbers to get a total or sum. It's one of the four basic operations in arithmetic and is symbolized by the plus sign (+). To add numbers together, you start with one number and then increase it by the amount of the next number.
For instance, in the expression $37 + 65 + 89 + 72 + 82$, each number is added to the sum of all the previous numbers. Here's a breakdown:

Start with 37.
Add 65 to 37, which totals 102.
Add 89 to 102, giving you 191.
Add 72 to 191, reaching 263.
Lastly, add 82 to 263, resulting in a final sum of 345.

This fundamental process of adding numbers is crucial in many areas of mathematics, including when calculating an average, which we'll cover later.

Division

Division is another core mathematical operation where you split a number into even parts. It's represented by the division sign (梅) or a fraction bar. In the context of finding an average, division is used to evenly distribute a total sum among the numbers you have.
After adding up the values in our initial problem to get 345, we divide this sum by the number of data points, which is 5. This means splitting 345 into five equal parts:

The division calculation used here is $345 \div 5$.
By performing this division, you find that each part, or the average, is 69.

Division helps us understand not only how things are portioned but also how they relate to each other in a more balanced way. It's a critical step in calculating averages, a common need in statistics.

Statistics

Statistics is a field of mathematics that deals with collecting, analyzing, interpreting, and presenting data. A crucial concept within statistics is the arithmetic mean, also known simply as the average.
When you want to find the average of a set of numbers, you follow these steps:

First, add up all the numbers鈥攁s we did with $37, 65, 89, 72, $ and $82$.
Then, divide this total by the count of numbers, which was 5 in our example.
This gives the arithmetic mean, which was 69 in this case.

Calculating the mean is a fundamental statistical tool. It gives you a central value that often represents your data set well. It's widely used in many fields, from economics to social sciences, to summarize large amounts of data effectively.

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91影视

Evaluate the expression. $$\frac{37+65+89+72+82}{5}$$

Short Answer

Step by step solution

Sum the Values

Divide by the Quantity

Key Concepts

Addition

Division

Statistics

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