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Chapter 14: Problem 55

Find the arithmetic mean for each set of values. $$ 5,9,8,2,4,7,3,2,0 $$

Short Answer

Expert verified
The arithmetic mean is approximately 4.44.

Step by step solution

01

Understand the Arithmetic Mean

The arithmetic mean (average) of a set of numbers is the sum of the numbers divided by the count of the numbers.
02

Sum the Values

Add all the given numbers together: \[5 + 9 + 8 + 2 + 4 + 7 + 3 + 2 + 0 = 40\]
03

Count the Values

Count how many values are in the set: There are 9 values.
04

Divide the Sum by the Count

Divide the sum of the numbers by the number of values: \[\frac{40}{9} \approx 4.44\]

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Key Concepts

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

average calculation
To calculate the arithmetic mean, follow a simple process. The mean is the sum of all items in a dataset divided by the number of items. It's commonly referred to as the 'average'.

Why is the average so helpful? It gives us a single number that represents the central point of a dataset, which can simplify comparisons and detect trends.
sum of numbers
Summing up numbers is a fundamental step in finding the mean.
Here's a quick way to add a list of numbers:

Use a methodical approach, where you add each number sequentially. For example, with the numbers 5, 9, 8, 2, 4, 7, 3, 2, and 0, add them step-by-step:

\[= 5 + 9 + 8 + 2 + 4 + 7 + 3 + 2 + 0 = 40\]

This systematic approach ensures that no number is skipped, helping avoid errors in calculation.
number count
Counting the number of items in a dataset is crucial for calculating the mean. Each item represents one count, even if the item is zero or repeated.

For example, in the dataset 5, 9, 8, 2, 4, 7, 3, 2, 0, there are exactly 9 numbers.

Once you've determined the count, use it as the denominator when dividing the sum of the numbers to find the mean: \[ Mean = \frac{Sum \ of \ the \ numbers}{Count \ of \ the \ numbers} = \frac{40}{9} \approx 4.44\]

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