Statistics and Probability

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Algebra › Statistics and Probability

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What is the mean given the following set? $x=[\frac{1}{2}, \frac{1}{4}, \frac{1}{6}]$

$\frac{11}{36}$

$\frac{11}{12}$

$\frac{11}{4}$

$\frac{1}{4}$

$\frac{4}{11}$

Explanation

To find the mean, add all the numbers in the set and divide by the total numbers in the set.

Convert $\frac{1}{2}+\frac{1}{4}+\frac{1}{6}$ to a common denominator and then add to find the total.

$\frac{1}{2}+\frac{1}{4}+\frac{1}{6} = \frac{6}{12}+\frac{3}{12}+\frac{2}{12} = \frac{11}{12}$

Dividing this sum by three is the same as multiplying the sum by one third.

$\frac{11}{12} \div 3 = \frac{11}{12}\times \frac{1}{3} = \frac{11}{36}$

The average is $\frac{11}{36}$ .

A class has a sum of test scores of . There are people in the class. What is the class average?

Cannot be determined

Explanation

Average is another way of describing mean. The mean represents the "central" value of a set of numbers. This is achieved by summing the numbers of a set and dividing it by the number of numbers in the set.

In this problem, the sum of all the scores is already provided. Because there are students, we can assume that is the sum of scores. Therefore, all we need to do is divide the sum by the number of scores.

$\frac{3871}{42}$

$=92.1667 \approx {\color{Blue} 92.2}$

Find the median of the following set of numbers:

$(2.55, 21, i^2, 56, 3.1, -55, \pi,\sqrt{2})$

where i is the imaginary number, $\sqrt{-1}$ .

Explanation

$(2.55, 21, 56, 3.1, -55, \pi,\sqrt{2} )$

First, rank the number in increasing order, remember $\pi\approx3.14$ and $ \sqrt{2}\approx 1.41 $ and $ i^2=-1$

$($ $-55, i^2, $ $\sqrt2 ,$ \$2.55 ,$ $ 3.1 ,$ $\pi,21 ,$ \$56)$

Since there is an even number of items in the set, the median is the averaege of the two center numbers:

Median:

Find the median of the following set of numbers:

$(2.55, 21, i^2, 56, 3.1, -55, \pi,\sqrt{2})$

where i is the imaginary number, $\sqrt{-1}$ .

Explanation

$(2.55, 21, 56, 3.1, -55, \pi,\sqrt{2} )$

First, rank the number in increasing order, remember $\pi\approx3.14$ and $ \sqrt{2}\approx 1.41 $ and $ i^2=-1$

$($ $-55, i^2, $ $\sqrt2 ,$ \$2.55 ,$ $ 3.1 ,$ $\pi,21 ,$ \$56)$

Since there is an even number of items in the set, the median is the averaege of the two center numbers:

Median:

What is the mean of and ?

$-\frac{1}{4}$

$\frac{1}{4}$

$-\frac{1}{2}$

$\frac{1}{2}$

Explanation

In order to find the mean of a set of numbers, we divide the sum of the numbers by the amount of numbers in the set. Since we have numbers in the set, we can calculate the mean as the following:

$\frac{4+(-4)+6+(-7)}{4}$

$=\frac{6-7}{4}$

$=-\frac{1}{4}$

A class has a sum of test scores of . There are people in the class. What is the class average?

Cannot be determined

Explanation

$\frac{3871}{42}$

$=92.1667 \approx {\color{Blue} 92.2}$

What is the mean given the following set? $x=[\frac{1}{2}, \frac{1}{4}, \frac{1}{6}]$

$\frac{11}{36}$

$\frac{11}{12}$

$\frac{11}{4}$

$\frac{1}{4}$

$\frac{4}{11}$

Explanation

To find the mean, add all the numbers in the set and divide by the total numbers in the set.

Convert $\frac{1}{2}+\frac{1}{4}+\frac{1}{6}$ to a common denominator and then add to find the total.

$\frac{1}{2}+\frac{1}{4}+\frac{1}{6} = \frac{6}{12}+\frac{3}{12}+\frac{2}{12} = \frac{11}{12}$

Dividing this sum by three is the same as multiplying the sum by one third.

$\frac{11}{12} \div 3 = \frac{11}{12}\times \frac{1}{3} = \frac{11}{36}$

The average is $\frac{11}{36}$ .

Find the mean: 4 4 2 3 3 2 3 1 1 2 3 2 2 2 1 14 2

Explanation

The sum of every data point is 51. There are 17 data points. 51 divided by 17 is 3.

What is the mean of the following dataset? $[\frac{8}{3},\frac{1}{3},\frac{6}{3}]$

$\frac{5}{3}$

$\frac{1}{5}$

$\frac{3}{5}$

Explanation

To find the mean, add all the numbers and divide by the total amount of numbers in the dataset.

$\frac{\frac{8}{3}+\frac{1}{3}+\frac{6}{3}}{3}$

Add the numerator.

$\frac{8}{3}+\frac{1}{3}+\frac{6}{3} = \frac{15}{3}=5$

Divide this by the denominator.

The mean is: $\frac{5}{3}$

What is the mean of and ?

$-\frac{1}{4}$

$\frac{1}{4}$

$-\frac{1}{2}$

$\frac{1}{2}$

Explanation

In order to find the mean of a set of numbers, we divide the sum of the numbers by the amount of numbers in the set. Since we have numbers in the set, we can calculate the mean as the following:

$\frac{4+(-4)+6+(-7)}{4}$

$=\frac{6-7}{4}$

$=-\frac{1}{4}$

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