Algebra II : Data Properties

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #1 : Median

Find the median of the following numbers:

11, 13, 16, 13, 14, 19, 13, 13

Possible Answers:

None of the other answers are correct.

Correct answer:

Explanation:

Reorder the numbers in ascending order (from lowest to highest):

11, 13, 13, 13, 13, 14, 16, 19

Find the middle number. In this case, the middle number is the average of the 4th and 5th numbers. Because both the 4th and 5th number are 13, the answer is simply 13.

Example Question #2 : Median

Find the median of this number set:  2, 15, 4, 3, 6, 11, 8, 9, 4, 16, 13

Possible Answers:

Correct answer:

Explanation:

List the numbers in ascending order: 2,3,4,4,6,8,9,11,13,15,16

The median is the middle number, or 8.

Example Question #13 : Median

A student has taken five algebra tests already this year. Her scores were , , , , and . What is the median of those values?

Possible Answers:

Correct answer:

Explanation:

To find the median of a set of values, simply place the numbers in order and find the value that is exactly "in the middle." Here, we can place the test scores in ascending order to get , , , , . (Descending order would work just as well.) The median is the middle value, . Make sure you don't confuse median with mean (average)! To get the mean value of this set, you would find the sum of the test scores and then divide by the number of values.

Example Question #4 : Median

What is the median of the following numbers?

12,15,93,32,108,22,16,21

Possible Answers:

Correct answer:

Explanation:

To find the median, first you arrange the numbers in order from least to greatest.

Then you count how many numbers you have and divide that number by two. In this case 12,15,16,21,22,32,93,108= 8 numbers.

So 

Then starting from the least side of the numbers count 4 numbers till you reach the median number of 

Then starting from the greatest side count 4 numbers until you reach the other median number of 

Finally find the mean of the two numbers by adding them together and dividing them by two 

to find the median number of .

Example Question #9 : Median

Cedric measured the height of his tomato plants, in centimeters, and collected the following data: 

What is the median height for his plants?

Possible Answers:

Correct answer:

Explanation:

First, arrange all of the data in numerical order: .

Then locate the middle number by using the formula

 , which gives you the location of the median in the ordered data set and where  is the number of terms in the data set.

Here, there are 11 terms.

So,  

Therefore, our number is the  one in the list, which is .

Example Question #11 : Median

If  and , then what could be the median of the whole set if all of them are arranged in increasing order?

Possible Answers:

Correct answer:

Explanation:

Since it's in increasing order, let's have some scenarios. Let's say  are both , then that means  at can be  with  maxing out its value up to  with  maxing its value. That leaves  must be  with  maxing out its value and  being in a range of  with  maxing its value and not violating the set. Now, lets say  are respectively, this leaves  only being  and  being  as well. Let's find the range of . If  were both , that means the median of them is . If  are both , that means the median of them is  is highest median of both  and  is the lowest median of . We need to find a number in the answer choices that fit this description. Answer is 

Example Question #14 : Median

What is the median of the first six cubic numbers?

 

Possible Answers:

Correct answer:

Explanation:

Cubic numbers are numbers taken to the third power. The first six cubic numbers are:  or 

Since, the numbers are inceasing, count the numbers in the set. There are six. Then divide six by two. We do this because we will split the number set in half. Because six does divide evenly into two, this means we can't easily determine the median. Since six divided by two is three, we are going to eliminate three numbers from leftmost in number set toward the right direction and three numbers from rightmost in number set toward the left direction. The last number crossed out in both direction are  and . To find the middle number, just add both numbers and divide by two.

 That.s the final answer.

Example Question #214 : Data Properties

Find the median.

Possible Answers:

Correct answer:

Explanation:

When finding the median, you are looking for the middle number. Always arrange the numbers in ascending order. Since, the numbers are inceasing, count the numbers in the set. There are five. Then divide five by two. We do this because we will split the number set in half. Because five doesn't divide evenly into two, this means we can easily determine the median. Since five divided by two is , we are going to eliminate two numbers from leftmost in number set toward the right direction and two numbers from rightmost in number set toward the left direction. The only number left is  and therefore is the right answer. 

Example Question #14 : Median

What is the median?

Possible Answers:

Correct answer:

Explanation:

When finding the median, you are looking for the middle number. Always arrange the numbers in ascending order. Since, the numbers are not in inceasing order, let's arrange it. It should look like: . Now, let's count the numbers in the set which is seven. Then divide seven by two. We do this because we will split the number set in half. Because seven doesn't divide evenly into two, this means we can easily determine the median. Since seven divided by two is , we are going to eliminate three numbers from leftmost in number set toward the right direction and three numbers from rightmost in number set toward the left direction. The only number left is  and therefore is the right answer. 

Example Question #15 : Median

What is the median?

Possible Answers:

Correct answer:

Explanation:

When finding the median, you are looking for the middle number. Always arrange the numbers in ascending order. Since, the numbers are inceasing, count the numbers in the set. There are six. Then divide six by two. We do this because we will split the number set in half. Because six does divide evenly into two, this means we can't easily determine the median. Since six divided by two is three, we are going to eliminate three numbers from leftmost in number set toward the right direction and three numbers from rightmost in number set toward the left direction. The last number crossed out in both direction are  and . To find the middle number, just add both numbers and divide by two.

 That's the final answer.

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