Data Properties - Algebra II

The range is the difference between the smallest number and the largest number. The smallest value is 77, and the largest is 98.

98 – 77 = 21

Let .

We know the mean is 8, and there are five values in the set, including the unknown .

Simplify.

Plug back into equation at top.

In order to find the mode, first we need to evaluate the function at each of our points:

Now we put our answers in order:

As we can see, the appears twice, which is more than any other number. Therefore the mode is .

In order to find the mode, first we need to evaluate the function at each of our points:

Now we put our answers in order:

As we can see, the appears twice, which is more than any other number. Therefore the mode is .

In order to find the mean, we would first add all the numbers up and divide by how many numbers we have. Though we don't yet know the value for , we do know the mean.

From here we can clear the denominator by multiplying each side by , and we can do most of the addition:

Now solving for :

Arrange the known values in the set in numerical order: {–5, –2, 1, 3, 5, 7, 7, 10}. The range is the difference between the largest value and smallest value.

x must be either the largest or the smallest value in the set.

range = x – smallest value

18 = x – (–5)

18 = x + 5

13 = x

OR

range = largest value – x

18 = 10 – x

8 = –x

–8 = x

Arrange the known values in the set in numerical order: {–5, –2, 1, 3, 5, 7, 7, 10}. The range is the difference between the largest value and smallest value.

x must be either the largest or the smallest value in the set.

range = x – smallest value

18 = x – (–5)

18 = x + 5

13 = x

OR

range = largest value – x

18 = 10 – x

8 = –x

–8 = x

The range is defined as the difference between the highest and lowest numbers in a set. Here, the highest number is and the lowest is .

Therefore, the range is

is the mode, is the mean, and 6 is the median.

In order to find the mean, we would first add all the numbers up and divide by how many numbers we have. Though we don't yet know the value for , we do know the mean.

From here we can clear the denominator by multiplying each side by , and we can do most of the addition:

Now solving for :

In order to find the mode, first we need to evaluate the function at each of our points:

Now we put our answers in order:

As we can see, the appears twice, which is more than any other number. Therefore the mode is .

Arrange the known values in the set in numerical order: {–5, –2, 1, 3, 5, 7, 7, 10}. The range is the difference between the largest value and smallest value.

x must be either the largest or the smallest value in the set.

range = x – smallest value

18 = x – (–5)

18 = x + 5

13 = x

OR

range = largest value – x

18 = 10 – x

8 = –x

–8 = x

The range is defined as the difference between the highest and lowest numbers in a set. Here, the highest number is and the lowest is .

Therefore, the range is

is the mode, is the mean, and 6 is the median.

In order to find the mean, we would first add all the numbers up and divide by how many numbers we have. Though we don't yet know the value for , we do know the mean.

From here we can clear the denominator by multiplying each side by , and we can do most of the addition:

Now solving for :

The range is the difference between the smallest number and the largest number. The smallest value is 77, and the largest is 98.

98 – 77 = 21

Arrange the known values in the set in numerical order: {–5, –2, 1, 3, 5, 7, 7, 10}. The range is the difference between the largest value and smallest value.

x must be either the largest or the smallest value in the set.

range = x – smallest value

18 = x – (–5)

18 = x + 5

13 = x

OR

range = largest value – x

18 = 10 – x

8 = –x

–8 = x

The median in the number in the middle of the data set.

Arrange the data in numerical order.

.

Therefore, the median is 21.

The median in the number in the middle of the data set.

Arrange the data in numerical order.

.

Therefore, the median is 21.

The median in the number in the middle of the data set.

Arrange the data in numerical order.

.

Therefore, the median is 21.

The median in the number in the middle of the data set.

Arrange the data in numerical order.

.

Therefore, the median is 21.

To find the mean, there are two steps:

1. Add all of the numbers in the set together.

2. Divide that number by the amount of numbers are in the set.

For this problem there are 13 numbers in the set, so we add the numbers together and divide by 13 to find the mean: