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Chapter 5: Problem 622

In the following exercises, find the mean of the numbers. $$ 2,4,1,0,1, \text { and } 1 $$

Short Answer

Expert verified
The mean is 1.5.

Step by step solution

01

Sum the Numbers

Add all the given numbers together: 2 + 4 + 1 + 0 + 1 + 1 = 9.
02

Count the Numbers

Determine the total number of values in the set. Here, there are 6 numbers.
03

Divide the Sum by the Number of Values

Divide the sum from Step 1 by the number of values from Step 2. The calculation is divide 9 by 6: \[\frac{9}{6} = 1.5.\]

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Key Concepts

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

Sum of Numbers
To calculate the mean, the first step is to find the sum of the numbers in the set. Sum means adding all the numbers together. For example, if you have the numbers 2, 4, 1, 0, 1, and 1:
You would add these like this: 2 + 4 + 1 + 0 + 1 + 1 = 9.
The sum is the total you get after adding. This gives you a single number that represents the combined value of all the numbers in the set.
Counting Values
The next step in finding the mean is counting how many numbers you have. This is crucial because the mean represents an average, and to find an average, you need to know how many values you are averaging.
In our example, the numbers given are: 2, 4, 1, 0, 1, 1. If you count each number, you will see there are 6 numbers in total.
So, we have 6 values in our set. It's important to ensure you count correctly to get the accurate mean.
Division for Mean
The final step is to divide the sum of the numbers by the number of values. This division gives you the mean, or the average value. In this step, you take the sum you previously calculated, which is 9, and divide it by the total count of numbers, which is 6.
The mathematical expression is \(\frac{9}{6}\).
When you do the division, \[ \frac{9}{6} = 1.5 \].
This means the mean of the numbers 2, 4, 1, 0, 1, and 1 is 1.5. This final number represents the average value of the set and summarizes the data set with a single, central value.

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Most popular questions from this chapter

The parking lot at the airport charges \(\$ 0.75\) for every 15 minutes. (a) How much does it cost to park for 1 hour? (b) Explain how you got your answer to part (a). Was your reasoning based on the unit cost or did you use another method?

Mollie had a 16 -ounce cappuccino at her neighborhood coffee shop. The cappuccino had 110 calories. If Mollie walks for one hour, she burns 246 calories. For how many minutes must Mollie walk to burn off the calories in the cappuccino? Explain your reasoning.

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