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Algebra 1 : Statistics and Probability

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #1544 : Algebra 1

You have spent money each month to ride the bus. You know in the last 6 months you have spent the following for each month:

$\$33.80, \$38.50, \$29.45, \$40.20, \$35.10, \$22.80$

You are interested to know what your average spending on busfare is and want to calculate the mean. Find the mean of your monthly bus ride expenses.

Possible Answers:

$\$33.31$

$\$27.32$

$\$52.11$

$\$32.20$

Correct answer:

$\$33.31$

Explanation:

To find the mean, you are finding the average of a set of values. The equation to find the mean is

$\overline{x}=\frac{\sum_{i=1}^{n}x_{i}}{n}$

where $x_{i}$ is one of the values you are averaging, and is the total number of data points. To make that equation look less intimidating, let's just put it into terms of our six data points. We are adding up all six of them and dividing by the total number of data points,

$\overline{x}=\frac{\left (x_{1}+x_{2}+x_{3}+x_{4}+x_{5}+x_{6} \right )}{6}$

$\overline{x}=\frac{\left (\$33.80+ \$38.50+ \$29.45+ \$40.20+ \$35.10+ \$22.80 \right )}{6}$

$\overline{x}=\frac{\$199.85}{6}$

$\overline{x}=\$33.3083 \approx \$33.31$

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Example Question #21 : Mean

Find the mean of the following set of numbers:

12,34,65,76,12,34,54,789,98,2,44,34

Possible Answers:

104.5

787

Correct answer:

104.5

Explanation:

Find the mean of the following set of numbers:

12,34,65,76,12,34,54,789,98,2,44,34

Finding the mean of a number set is essentially finding the average.

Begin by summing the numbers, then divide by the total number of terms.

12+34+65+76+12+34+54+789+98+2+44+34=1254

Now, since there are 12 terms in the series, divide by 12

$\frac{1254}{12}=104.5$

So our mean is 104.5

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Example Question #121 : Statistics And Probability

A groups of students were studying the beak sizes of soapberry bugs. They collected data on the lengths of their beaks. What is the average of their number set?

6.3mm,6.7mm,5.4mm,5.2mm,6.1mm,5.7mm,6.6mm,6.5mm,5.8mm,5.9mm

Possible Answers:

5.7mm

5.3mm

5.0mm

5.8mm

6.0mm

Correct answer:

6.0mm

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, we are given five scores. In order to begin this problem, we must take the sum of the lengths.

6.3+6.7+5.4+5.2+6.1+5.7+6.6+6.5+5.8+5.9=60.2

Now in order to find the mean, we must divide this number by the number of measurements.

$\frac{60.2}{10}$

$={\color{Blue} 6.02 \approx 6.0}$

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Example Question #123 : Statistics And Probability

Find the mean of the following number set:

147,22,465,7,33,465,88,97,102,22,1,109,465

You may round to the nearest whole number.

Possible Answers:

156

464

106

Correct answer:

156

Explanation:

Find the mean of the following number set:

147,22,465,7,33,465,88,97,102,22,1,109,465

The mean is the same thing as the average. To find the average of a set of numbers, add them up and then divide by the total number of items in the series.

Now, there are 13 terms, so we need to divide by 13.

$\frac{2023}{13}\approx =155.6\approx156$

So our answer is 156

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Example Question #124 : Statistics And Probability

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

Possible Answers:

$\frac{11}{36}$

$\frac{11}{12}$

$\frac{1}{4}$

$\frac{4}{11}$

$\frac{11}{4}$

Correct answer:

$\frac{11}{36}$

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 $\frac{11}{36}$ .

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Example Question #125 : Statistics And Probability

Find the mean of the following dataset: [x,x+y,3x,2x]

Possible Answers:

$\frac{7x+y}{4}$

$\frac{7x+y}{5}$

$\textup{There is no mean.}$

$\frac{7x}{5}+y$

$\frac{7x}{4}+y$

Correct answer:

$\frac{7x+y}{4}$

Explanation:

The mean is the sum of all the numbers or variables existent in the data set divided by the number of terms in the dataset.

Add all four terms and combine like terms.

x+x+y+3x+2x= 7x+y

Divide this value by four.

The average is: $\frac{7x+y}{4}$

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Example Question #121 : How To Find Mean

Find the mean of the dataset: [6,2,7,1]

Possible Answers:

6.5

5.5

Correct answer:

Explanation:

The mean is the sum of all numbers divided by the total numbers in the dataset.

Add the numbers.

6+2+7+1 = 16

Divide this number by four.

$\frac{16}{4}=4$

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Example Question #122 : How To Find Mean

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

Possible Answers:

2.94

3.06

2.82

Correct answer:

Explanation:

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

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Example Question #123 : How To Find Mean

Find the mean of the following set of numbers.

1,4,5,5,6,15,15,16,23

Possible Answers:

Correct answer:

Explanation:

To solve, simply sum the numbers and divide by the quantity. Thus,

$mean=\frac{1+4+5+5+6+15+15+16+23}{9}=\frac{90}{9}=10$

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Example Question #129 : Statistics And Probability

Find the mean: $[\frac{1}{2}, 0.3, 4\%]$

Possible Answers:

0.28

0.5

0.84

2.4

0.3

Correct answer:

0.28

Explanation:

The mean is the sum of all numbers in the set divided by the total of numbers in the set.

In order to add these numbers, we will need to choose a conversion for all numbers. Let's choose decimal for simplicity.

Convert $\frac{1}{2}$ to a decimal.

$\frac{1}{2}=0.5$

Convert $4\%$ to a decimal. Remove the percentage and move the decimal place back two spaces.

$4\% = 0.04$

Add the numbers.

0.5+0.04+ 0.3 = 0.84

Divide this number by the total number in the set, .

$\frac{0.84}{3} = 0.28$

The mean is: 0.28

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Algebra 1 : Statistics and Probability

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1544 : Algebra 1

Example Question #21 : Mean

Example Question #121 : Statistics And Probability

Example Question #123 : Statistics And Probability

Example Question #124 : Statistics And Probability

Example Question #125 : Statistics And Probability

Example Question #121 : How To Find Mean

Example Question #122 : How To Find Mean

Example Question #123 : How To Find Mean

Example Question #129 : Statistics And Probability

All Algebra 1 Resources

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