Algebra II - Data Properties

Determine the mean of the numbers:

$\textup{The mean cannot be determined.}$

Explanation

Add all the numbers.

The mean is the average of all the numbers, which means dividing this number by five will give the average.

$\frac{160}{5} =32$

The answer is:

Determine the range of the following numbers:

Explanation

The range is defined as the difference of the highest and lowest numbers.

The highest number is 41.

The lowest number is 3.

Subtract both numbers.

The answer is:

Determine the range of the numbers:

Explanation

The range is the difference between the highest and lowest numbers.

The highest number is 11.

The smallest number is negative three.

Subtract both numbers. Use parentheses to embrace the negative value.

The answer is:

Determine the mean of the numbers: $[\frac{1}{3},3%, \frac{1}{30}]$

$\frac{119}{900}$

$\frac{119}{300}$

$\frac{1}{30}$

$\frac{19}{30}$

$\frac{19}{90}$

Explanation

The mean is the average of all the numbers. Convert the percentage to a fraction by removing the percentage and divide the number by 100.

$[\frac{1}{3},3%, \frac{1}{30}]\rightarrow[\frac{1}{3}, \frac{3}{100},\frac{1}{30}]$

Convert all fractions to a common denominator. Write out the factors for the denominators.

The common denominator is 300.

$\frac{1}{3}+ \frac{3}{100}+\frac{1}{30}= \frac{1(100)}{3(100)}+ \frac{3(3)}{100(3)}+\frac{1(10)}{30(10)}$

Simplify the fractions.

$\frac{100}{300}+\frac{9}{300}+\frac{10}{300} = \frac{119}{300}$

There are three numbers in the data set. Divide the fraction by three.

$\frac{ \frac{119}{300}}{3}= \frac{119}{300} \div 3 = \frac{119}{300}\times \frac{1}{3} = \frac{119}{900}$

The answer is: $\frac{119}{900}$

Determine the range of the numbers:

Explanation

The range is the difference between the highest and lowest numbers.

The highest number is 11.

The smallest number is negative three.

Subtract both numbers. Use parentheses to embrace the negative value.

The answer is:

Determine the range of the following numbers:

Explanation

The range is defined as the difference of the highest and lowest numbers.

The highest number is 41.

The lowest number is 3.

Subtract both numbers.

The answer is:

Determine the mean of the numbers:

$\textup{The mean cannot be determined.}$

Explanation

Add all the numbers.

The mean is the average of all the numbers, which means dividing this number by five will give the average.

$\frac{160}{5} =32$

The answer is:

Determine the mean of the numbers: $[\frac{1}{3},3%, \frac{1}{30}]$

$\frac{119}{900}$

$\frac{119}{300}$

$\frac{1}{30}$

$\frac{19}{30}$

$\frac{19}{90}$

Explanation

The mean is the average of all the numbers. Convert the percentage to a fraction by removing the percentage and divide the number by 100.

$[\frac{1}{3},3%, \frac{1}{30}]\rightarrow[\frac{1}{3}, \frac{3}{100},\frac{1}{30}]$

Convert all fractions to a common denominator. Write out the factors for the denominators.

The common denominator is 300.

$\frac{1}{3}+ \frac{3}{100}+\frac{1}{30}= \frac{1(100)}{3(100)}+ \frac{3(3)}{100(3)}+\frac{1(10)}{30(10)}$

Simplify the fractions.

$\frac{100}{300}+\frac{9}{300}+\frac{10}{300} = \frac{119}{300}$

There are three numbers in the data set. Divide the fraction by three.

$\frac{ \frac{119}{300}}{3}= \frac{119}{300} \div 3 = \frac{119}{300}\times \frac{1}{3} = \frac{119}{900}$

The answer is: $\frac{119}{900}$

Determine the mean of the data set: $[\frac{2}{5}, \frac{1}{3}, \frac{7}{4},-2]$

$\frac{29}{240}$

$\frac{269}{240}$

$\frac{37}{120}$

$\frac{47}{120}$

$\frac{59}{240}$

Explanation

The mean is the sum of the numbers in the data set.

Add all the numbers. To add the fractions, we will need to find the least common denominator.

Multiply all the denominators together.

$5\times 3\times 4 = 60$

Convert all the numbers with a denominator of 60. What is multiplied on the bottom must be multiplied on the top as well.

$\frac{2}{5}+\frac{1}{3}+ \frac{7}{4}+(-2) = \frac{2(4)(3)}{5(4)(3)}+\frac{1(4)(5)}{3(4)(5)}+\frac{7(3)(5)}{4(3)(5)}-\frac{2(4)(3)(5)}{1(4)(3)(5)}$

Simplify all the fractions.

$\frac{24}{60}+\frac{20}{60}+\frac{105}{60}-\frac{120}{60} = \frac{29}{60}$

Divide this fraction by four to find the mean. Dividing by four is the same as multiplying by one-fourth.

$\frac{29}{60}\times \frac{1}{4} = \frac{29}{240}$

The answer is: $\frac{29}{240}$

Reginald has scores of {87, 79, 95, 91} on the first four exams in his Spanish class. What is the minimum score he must get on the fifth exam to get an A (90 or higher) for his final grade?

Explanation

To find the fifth score, we need to set the average of all of the scores equal to 90.

$\frac{(87+79+95+91+x)}{5}=90$

$\frac{(352+x)}{5}=90$

Multiply both sides of the equation by 5.

Subtract 352 from both sides of equation.

Data Properties

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