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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #153 : How To Find Median

Solve for the median: [-2,-9,5,1]

Possible Answers:

$-\frac{1}{2}$

$\textup{The median does not exist.}$

$\frac{1}{2}$

Correct answer:

$-\frac{1}{2}$

Explanation:

The median is the central number of a chronologically ordered data set from least to greatest.

Reorder the data set.

$[-2,-9,5,1]\rightarrow [ -9,-2,1,5]$

Since there are four numbers in the data set, the median is the average of the two central numbers.

$\frac{-2+1}{2} = -\frac{1}{2}$

The median is: $-\frac{1}{2}$

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Example Question #151 : How To Find Median

Find the median of the data set: [-9,10,-8,7,6]

Possible Answers:

$\frac{6}{5}$

Correct answer:

Explanation:

The median of this set is the central number of the chronological ordered numbers from least to greatest.

Reorder the numbers from least to greatest.

$[-9,10,-8,7,6]\rightarrow[-9,-8,6,7,10]$

The median is .

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Example Question #155 : How To Find Median

Find the median: [-5,9,-3,10,11,12]

Possible Answers:

$\frac{17}{2}$

$\frac{17}{3}$

$\frac{19}{2}$

$\frac{7}{2}$

Correct answer:

$\frac{19}{2}$

Explanation:

To find the median, first reorganize all the numbers in chronological order.

$[-5,9,-3,10,11,12]\rightarrow [-5,-3,9,10,11,12]$

Average the center two numbers of the even number data set.

$\frac{9+10}{2} = \frac{19}{2}$

The median is: $\frac{19}{2}$

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Example Question #156 : How To Find Median

On a recent algebra test, students achieved the following scores:

Student 1:

Student 2:

Student 3:

Student 4:

Student 5:

Student 6:

Student 7:

Student 8:

Student 9:

Student 10: 100

Student 11:

What is the median score?

80, 80, 95, 90, 90, 70, 65, 85, 90, 100, 50

50, 65, 70, 80, 80, 85, 90, 90, 90, 95, 100

Possible Answers:

Correct answer:

Explanation:

The easiest way to begin this problem is to put the scores in numerical order:

50,65,70,80,80,85,90,90,90,95,100

The median is the middle score. In this case, that answer is .

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Example Question #157 : How To Find 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, $\sqrt{-1}$ .

Possible Answers:

5.65

2.825

2.55

0.5

3.1

Correct answer:

2.825

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:

(2.55+3.1)/2=2.825

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Example Question #361 : Statistics And Probability

Find the median of the following data set:

23, 24, 26, 32, 31, 32, 22, 21, 20, 30

Possible Answers:

26.1

Correct answer:

Explanation:

List the values in numerical order:

20, 21, 22, 23, 24, 26, 30, 31, 32, 32

Find the middle two numbers:

24, 26

Find the average of the middle numbers by adding them and dividing by 2:

24+26 = 50

$50\div 2 = 25$

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Example Question #1 : How To Find Mode

When rolling two standard six-sided dice, what is the probability of NOT getting a seven?

Possible Answers:

$\frac{5}{12}$

$\frac{1}{4}$

$\frac{2}{3}$

$\frac{5}{6}$

$\frac{1}{6}$

Correct answer:

$\frac{5}{6}$

Explanation:

When rolling two six-sided dice there are possible outcomes.

$6\ \textup{outcomes of die 1}*6\ \textup{outcomes of die 2}=36\ \textup{possible outcomes}$

The possible combinations to get a seven are: $1,6\; \; \; 2,5\; \; \; 3,4\; \; \; 4,3\; \; \; 5,2\; \; \; 6,1$ .

So there are six ways to get a seven, out of combinations total. The resulting probability of getting a seven is $\frac{6}{36}= \frac{1}{6}$ .

The probability of NOT getting a seven is $1-\frac{1}{6}= \frac{5}{6}$ .

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Example Question #2 : How To Find Mode

A short quiz with 5 questions is given to a class of 30 students. 7 students answered 5 questions correctly, 12 students answered 4 questions correctly, 9 students answered 3 questions correctly, and 2 students answered 2 questions correctly.

What is the mode among the class's scores?

Possible Answers:

3.8

3.5

Correct answer:

Explanation:

The mode is the value that appears most often in a set of data. Within the class, 7 students answered 5 questions correctly, 12 students answered 4 questions correctly, 9 students answered 3 questions correctly, and 2 students answered 2 questions correctly. More students scored a 4 than any other score, so this score is the class's mode.

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Example Question #1 : How To Find Mode

Which of the following data sets has exactly one mode regardless of the value of ?

Possible Answers:

$\{ 3, 7, 8, 9, 10, 10, 10, 10, 11, 11, 13, N \}$

$\{ 7, 8, 9, 10, 10, 11, 11, 13, N \}$

$\{ 9, 10, 10, 10, 10, 11, 11, 13, N, N \}$

$\{ 1, 2, 3, 4, 5, 6, 7, 8, 9, N \}$

$\{ 8, 8, 8, N, N, N \}$

Correct answer:

$\{ 3, 7, 8, 9, 10, 10, 10, 10, 11, 11, 13, N \}$

Explanation:

$\{ 3, 7, 8, 9, 10, 10, 10, 10, 11, 11, 13, N \}$ is the correct set; no matter what is, no value other than 10 can appear four or more times.

To see that no other choice works, let's examine them.

$\{ 7, 8, 9, 10, 10, 11, 11, 13, N \}$ : If is any number other than 10 or 11, then the number has 10 and 11, and possibly one other number, as modes, each appearing twice.

$\{ 1, 2, 3, 4, 5, 6, 7, 8, 9, N \}$ : If is not any of the numbers already in the set, the set has no repeated values and thus no mode.

$\{ 8, 8, 8, N, N, N \}$ : If $N \neq 8$ , then the set is bimodal, with 8 and the modes.

$\{ 9, 10, 10, 10, 10, 11, 11, 13, N, N \}$ : If N = 11 , the set is bimodal, with 10 and 11 the modes.

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Example Question #2 : How To Find Mode

Find the mode of the following set of numbers: 2, 8, 4, 9, 2.

Possible Answers:

Correct answer:

Explanation:

The mode of a set of numbers is the number that appears the most. In this set of numbers, 2 appears twice, and all of the other numbers appear only once. Thus, 2 is the mode of this set of numbers.

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #153 : How To Find Median

Example Question #151 : How To Find Median

Example Question #155 : How To Find Median

Example Question #156 : How To Find Median

Example Question #157 : How To Find Median

Example Question #361 : Statistics And Probability

Example Question #1 : How To Find Mode

Example Question #2 : How To Find Mode

Example Question #1 : How To Find Mode

Example Question #2 : How To Find Mode

All Algebra 1 Resources

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