Algebra 1 : How to find mean

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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Example Question #201 : Statistics And Probability

Given the following data, find the range, mode, and mean: 

Possible Answers:

Correct answer:

Explanation:

Luckily, we are provided with a data set that is already in numerical order: 

.

To find the range, we subtract the lowest value from the highest, 

.

To find the mean, we add all of the data pieces and divide by the number of data pieces, 

.

To find the mode, we search for numbers tha appear more than once. Since none of these data values appear more than once, we have no mode. 

Example Question #21 : Basic Statistics

Sally's algebra grade depends on three unit tests and a final exam. The grade for the final exam is weighted to equal the grade of two unit tests. What is the minimum grade that Sally must get on her final exam in order to have a class average of  or above for the course, if her unit test scores are , , and 

Possible Answers:

Correct answer:

Explanation:

The course grade average is calculated by using Sally's three test scores and final exam. student must score at least an average of ; therefore we can write the following:

Given that the average is calculated using three test scores and a final weighted as two regular tests, we can write the following equation. 

Let's use these equations to construct an inequality where we will substitute in our known values and let a variable, , equal the final score needed to earn an a  or above.

Sally needs to at least score a  on the final to score  or above.

Example Question #203 : Statistics And Probability

Alex set up a lemonade stand on Saturday morning, and tracked how much money he earned each hour for four hours. The mean amount of money that he earned per hour was . The first hour he earned , the second hour he earned , and the third hour he earned . How much money did he earn during the fourth hour?

Possible Answers:

$8.00

$7.50

$6.25

$9.25

$6.75

Correct answer:

$7.50

Explanation:

In order to find out how much money Alex earned during the fourth hour, we need to understand how to find the mean of a set of numbers (also known as the 'average'). To find the mean of any set of numbers, we first add together all of the numbers in the set to find a total sum, and then we divide this sum by the amount of numbers that are in the set:

 

Let's look at the information given to us in this problem. We know several things:

- The mean amount of money that Alex earned each hour was 

- Alex worked for a total of 

- The amount of money earned for three out of four of the hours (; ; )

 

We DON'T know how much money Alex earned during the 4th hour, but we can figure it out by plugging in what we know into the equation for finding the mean of a set, as follows:

 

 

For "Mean", we plug in the mean amount that Alex earned (which was ). For "sum of all numbers" we plug in the amount that Alex earned for every hour, and add them all together. Since we only know how much money Alex earned for three out of the four hours, we'll use  as a placeholder for the fourth hour. For "amount of numbers in set", we plug in , since that is the total number of hours that Alex worked.

Now, all we need to do is solve for . We'll do this by first adding together all of the numbers in the numerator of our fraction:

 

 

Next, we multiply both sides of our equation by , in order to get rid of our fraction:

 

 

Finally, subtract  from both side to get  by itself:

 

 

So,  is our answer. 

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