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Chapter 5: Problem 362

Find the mean. $$525,532,558,574$$

Short Answer

Expert verified
The mean is 547.25.

Step by step solution

01

Add All Numbers

Sum all the given numbers: ewline525 + 532 + 558 + 574 = 2189.
02

Count the Numbers

Determine how many numbers are in the set. Here, there are four numbers.
03

Divide the Sum by the Number of Items

Divide the sum obtained in Step 1 by the number of items found in Step 2: ewline \(\text{Mean} = \frac{2189}{4} = 547.25\)

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Key Concepts

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

average
The concept of an 'average' is one of the most fundamental in statistics. It provides a single value that gives insight into a set of numbers. Think of the average as the 'middle point' of the data.
To calculate the average, we use a simple formula: we add up all the numbers in a set (this sum tells us the cumulative total), and then we divide this sum by the number of items in the set. This helps us understand the overall tendency or general pattern in the data.
For example, consider the set of numbers given in the exercise: 525, 532, 558, and 574. The average here tells us where the central value of these four numbers lies.
sum of numbers
Calculating the sum of a set of numbers is the first step in finding the average. The sum is simply the result of adding all numbers together.
The exercise involves the numbers 525, 532, 558, and 574. To find the sum of these numbers:
  • Add 525 to 532, which gives 1057
  • Add 558 to this result: 1057 + 558 = 1615
  • Finally, add 574 to this: 1615 + 574 = 2189
So, the total sum of these numbers is 2189. This number is crucial because it represents the combined total of all elements in the set and is needed for the next step: dividing to find the average.
dividing
The final step in finding the average involves dividing the sum of all numbers by the number of items in the set. This 'division' step gives us the average.
From the previous section, we know the sum of our numbers is 2189. Since there are four numbers in the set, we divide 2189 by 4.
The equation looks like this: \(\text{Average} = \frac{2189}{4} = 547.25\).
Here, 547.25 is the average value of our set. This means that if the four numbers were evenly distributed, each would approximately be 547.25. The division step is critical to determine this middle point value.

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