Algebra 1 : Statistics and Probability

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #51 : Statistics And Probability

If the average of  numbers is  and the average of  numbers is , what is the average of the other  numbers?

Possible Answers:

Correct answer:

Explanation:

If the average of  numbers is , the sum becomes .

If the average of the  numbers is , then the sum is .

This makes the sum of the other two numbers to be .

Then the average of those two numbers is 

Example Question #52 : How To Find Mean

If the average of  numbers is  and the average of  numbers is , what is the sum of the other numbers?

Possible Answers:

Correct answer:

Explanation:

If the average of  numbers is , the sum becomes .

If the average of the  numbers is , then the sum is .

This makes the sum of the other three numbers to be 

Example Question #53 : Statistics And Probability

What is the average angle of a square?

Possible Answers:

Correct answer:

Explanation:

The total degree of a square is .

Since a square has four angles, we divide  and  to get 

Example Question #51 : Statistics And Probability

If Joe took three exams and scored , what must he score on the final exam to get an average of ?

Possible Answers:

Correct answer:

Explanation:

We need an average of  for four exams.

That means the sum of his exams must be  or .

We know the sum of his three exams which is .

The difference is 

Example Question #51 : Statistics And Probability

What is the average of the first four prime numbers?

Possible Answers:

Correct answer:

Explanation:

The first four prime numbers are .

The sum is .

Since there are four numbers, the average is 

Example Question #51 : Statistics And Probability

Find the mean of the following numbers (round to the nearest tenth). 

Possible Answers:

Correct answer:

Explanation:

Add every number together and divide by the total number of numbers in the set (9) to get the following.

  

Example Question #52 : Statistics And Probability

Find the mean of .

Possible Answers:

Correct answer:

Explanation:

The mean is the average of a set of numbers. The mean is found by adding up all of the numbers in the set and then dividing by the size of the set. There are numbers in the set. The sum of number is . The mean is  divided by  which is .

Example Question #51 : Statistics And Probability

The mean of a data set is the average value of all values in the set.

James is taking a class which has 5 exams over the semester. James has already taken 3 exams, and his scores are 78, 85, and 96. If James wants to average at least 80 across all 5 exams, what is the average score he must have for his final 2 exams?

Possible Answers:

Correct answer:

Explanation:

Solving this question involves understanding how the equation for mean of a data set works. Let's look at the data set so far:

Since all the elements of this data set are the same (test scores), let's call the missing values t.

We know we want our final average to be an 80, so let's look at the basic equation for finding mean, with 80 in place of x:

At this point, simple algebra takes over:

 Multiply both sides by 5.

 Subtract known values from the right side and simplify.

 Simplify.

Thus, James must score an average of 70.5 on each of his remaining tests to average an 80 for the semester. This could mean he scores a 70 and 71, or a 90 and a 51, or any combination of scores that averages to at least 70.5. (By the looks of it, James is in good shape!)

Example Question #52 : Statistics And Probability

The mean of a data set is the average value of all values in the set.

Annie is budgeting for the holidays, and is trying to figure out how much money se should set aside to buy gifts for her family.

Over the last five years, she has spent  and  on gifts. How much, on average, should Annie plan to save for gift-giving this year?

Possible Answers:

Correct answer:

Explanation:

To find the average cost of gifts, we simply sum all of our data points, then divide by the total number of points. In this case, we have an  of 5, so we'll have 5 numbers to play with and we'll be dividing by 5 at some point.

Some people will want to rearrange the numbers from least to greatest, but this is not strictly necessary for calculating the mean.

So on average, Annie will need to save  this year.

Example Question #51 : Statistics And Probability

Using the data above, find the mean. 

Possible Answers:

Correct answer:

Explanation:

To find the mean, or average, of a set of data simply find the sum of all of the data and divide the total by the amount of data pieces (n), 

.

So for this set of data, 

.

11 is our average. (note that unlike finding the median and mode, the mean is not necessarily a piece of data currently in the data set)

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