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Algebra 1 : Statistics and Probability

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Example Questions

Example Question #171 : Statistics And Probability

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

Possible Answers:

$\frac{3}{5}$

$\frac{1}{5}$

$\frac{5}{3}$

Correct answer:

$\frac{5}{3}$

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: $\frac{5}{3}$

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Example Question #171 : Statistics And Probability

If Sam's three of the four exam grades in algebra class were 75,90,45 and he needs to average a to pass the class, what minimum score must he make on the fourth exam to pass the class?

Possible Answers:

$\textup{Sam will pass with or without Exam 4.}$

Correct answer:

Explanation:

The mean of Sam's four scores must be at least 70. Set up an equation such that the three exam scores plus the fourth exam score over four equals 70.

$\frac{75+90+45+x}{4}=70$

The variable is the unknown exam score. Multiply four on both sides to eliminate the denominator.

$\frac{75+90+45+x}{4} \cdot 4=70 \cdot 4$

75+90+45+x = 280

Solve for .

210+x = 280

Subtract 210 on both sides.

210+x -210= 280-210

Simplify.

x=70

Sam must make at least a 70 on his next exam to pass.

The answer is:

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Example Question #171 : Statistics And Probability

Find the mean of the dataset: [5,8,-3,-4]

Possible Answers:

$\frac{16}{3}$

$\frac{7}{2}$

$\frac{3}{2}$

$\frac{13}{4}$

Correct answer:

$\frac{3}{2}$

Explanation:

To find the mean of the dataset, we will need to add all the numbers and divide by the total numbers existing in the dataset.

$\frac{5+8+(-3)+(-4)}{4}=\frac{13-7}{4} = \frac{6}{4} = \frac{3}{2}$

The answer is: $\frac{3}{2}$

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Example Question #174 : Statistics And Probability

Let , , and be the mean, median, and mode, respectively, of the dataset

$\left \{ 1, 2, 4, 4, 4, 5, 6, 7, 8 \right \}$ .

Which of the following correctly relates , , and ?

Possible Answers:

B< A < C

A < B < C

A = B = C

A< B = C

B = C < A

Correct answer:

B = C < A

Explanation:

The mean of a dataset is the sum of the entries divided by the number of entries. The mean of this nine-entry dataset is

$A = ( 1+ 2+ 4+ 4+ 4+ 5+ 6+ 7+ 8 ) \div 9 = 41 \div 9 = 4 \frac{5}{6}$

The median of an arranged dataset with an odd number of elements is its middle element. The dataset is arranged and has nine elements; this middle element is B = 4 .

The mode of a dataset is the element that appears the most frequently, In this set, the element 4 appears the most times, three, so C= 4 is the mode.

The correct ordering is B = C < A .

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Example Question #175 : Statistics And Probability

What is the mean of the dataset? $[\sqrt2, \sqrt 9, \sqrt4]$

Possible Answers:

$\frac{ \sqrt7}{3}$

$\frac{ \sqrt{10}}{3}$

$\frac{ 5\sqrt2 }{3}$

$\frac{ \sqrt2 +5}{3}$

$\frac{\sqrt{38}}{3}$

Correct answer:

$\frac{ \sqrt2 +5}{3}$

Explanation:

Two of the radicals can be simplified. The $\sqrt2$ term is irrational and cannot be simplified any further.

$[\sqrt2, \sqrt 9, \sqrt4] = [\sqrt2,3,2]$

Add up the numbers.

$\sqrt2+3+2 = \sqrt2 +5$

Divide this quantity by three.

The answer is: $\frac{ \sqrt2 +5}{3}$

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Example Question #176 : Statistics And Probability

Find the mean of the following dataset: [1,6,4,10,4]

Possible Answers:

Correct answer:

Explanation:

Add the numbers and divide by the total amount of numbers in the dataset.

$\frac{1+6+4+10+4}{5}$

Simplify this fraction.

$\frac{25}{5}=5$

The answer is:

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Example Question #177 : Statistics And Probability

Find the mean of the following data set:

33, 7, 22, 1, 29, 8, 13, 7

Possible Answers:

Correct answer:

Explanation:

To find the mean of a data set, we use the following formula:

$\text{mean} = \frac{\text{sum of numbers}}{\text{quantity of numbers}}$

Given the data set, we know

$\text{mean} = \frac{33+7+22+1+29+8+13+7}{8}$

$\text{mean} = \frac{120}{8}$

$\text{mean} = 15$

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Example Question #172 : Statistics And Probability

Find the mean of the dataset: [5,8,10,3,26]

Possible Answers:

$\textup{No mean.}$

$\frac{52}{5}$

$\frac{62}{5}$

$\frac{42}{5}$

Correct answer:

$\frac{52}{5}$

Explanation:

The mean is the average of all the numbers given in the dataset.

Add all the integers given in the dataset.

5+8+10+3+26 = 52

Divide this number by the total numbers in the dataset.

The answer is: $\frac{52}{5}$

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Example Question #172 : Statistics And Probability

Determine the mean for the following dataset: [2,9,6,3,8]

Possible Answers:

$\frac{38}{5}$

$\frac{28}{5}$

$\frac{29}{5}$

Correct answer:

$\frac{28}{5}$

Explanation:

The mean is the average of all the numbers in the dataset.

Add all the numbers.

2+9+6+3+8+= 28

Divide this number by the total amount of numbers in the dataset.

The answer is: $\frac{28}{5}$

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Example Question #180 : Statistics And Probability

A test was given to a class of students. The average for the class was .Two students scored 100 , two scored , two scored and two scored . For the remaining two students, one scored twice as much as the other. How much did the two remaining students score?

Possible Answers:

40,80

37.5,75

50,100

45,90

43,86

Correct answer:

40,80

Explanation:

It is clear that among the remaining two students, one scored lower than the other. Let the lower score of the remaining student be . Then the higher of the two scores is (as is twice as much as ). We want to find the values for and .

The sum of scores for the students is 630 . We know that average score (Here ) is sum of all the scores (Here 630+x+2x = 630+3x )divided by the total number of scores (Here ).

$\frac{630+3x}{10}=75$

630+3x=750

3x=750-630=120

$x=\frac{120}{3}=40$

2x= 2(40)=80

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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 #171 : Statistics And Probability

Example Question #171 : Statistics And Probability

Example Question #171 : Statistics And Probability

Example Question #174 : Statistics And Probability

Example Question #175 : Statistics And Probability

Example Question #176 : Statistics And Probability

Example Question #177 : Statistics And Probability

Example Question #172 : Statistics And Probability

Example Question #172 : Statistics And Probability

Example Question #180 : Statistics And Probability

All Algebra 1 Resources

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