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Chapter 1: Problem 92

Find the average of each list of numbers. $$121,200,185,176,163$$

Short Answer

Expert verified
The average is 169.

Step by step solution

01

Determine the Total Sum

Add up all the numbers in the list to determine the total sum. The numbers are 121, 200, 185, 176, and 163. Calculate the total:\[ 121 + 200 + 185 + 176 + 163 = 845 \]
02

Count the Numbers in the List

Count how many numbers are in the list. In this case, there are five numbers.
03

Calculate the Average

To find the average, divide the total sum of the numbers by the number of values in the list. Use the formula for average:\[ \text{Average} = \frac{\text{Total Sum}}{\text{Number of Items}} = \frac{845}{5} = 169 \]

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Key Concepts

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

Total Sum
Finding the total sum is the first step in calculating the average. It's like adding up the scores in a game to see your overall performance. In our example, you have the numbers 121, 200, 185, 176, and 163.
  • Start by stacking these numbers together. Add them up one by one.
  • This can sometimes look like a long process, but it's essential to ensure accuracy.
  • After adding them, you get the total sum of 845.
Visualize this process as if you were building a tower with blocks. Each block (or number) adds up to reach the top, which in this case, is 845. Getting the total sum right is crucial because it serves as the foundation for finding your final average.
Number of Items
Once you have the total sum, the next key step is determining how many numbers you are dealing with. Counting items might seem trivial, but it provides the scale of your data set. In our example, you have five numbers in the list:
  • 121
  • 200
  • 185
  • 176
  • 163
Remember, each number represents a separate item or unit in your collection. Knowing the number of items is necessary for calculating the average, as it helps in dividing the total sum properly. Think of it like counting apples in a basket before sharing them. You'll want to know how many there are to divide them evenly among your friends.
Division
The final step in finding the average is using division. This step combines the efforts from gathering the total sum and counting the number of items. Think of division as a way to distribute something fairly among all parts. Here鈥檚 how it works:
  • With the total sum of 845 and 5 numbers, divide 845 by 5.
  • Use the formula: \( \text{Average} = \frac{\text{Total Sum}}{\text{Number of Items}} \)
  • In this case: \( 845 \div 5 = 169 \)
So, the average of your list is 169. Division ensures that all quantities are evenly distributed, providing a balanced representation of your data. Just like slicing a pie into equal parts for everyone at the table, division in averages shares the total sum equally among the number of items.

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