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Algebra II : Basic Statistics

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Example Questions

Example Question #38 : Median

Find the median of the following data set:

66,123,44,78,99,67,143,44,107,12,578,12,67,367,44

Possible Answers:

114

566

Correct answer:

Explanation:

Find the median of the following data set:

66,123,44,78,99,67,143,44,107,12,578,12,67,367,44

Let's begin by putting our data in increasing order:

12,12,44,44,44,66,67,67,78,99,107,123,143,367,578

Now, the median should be pretty straightforward to find.

The median will simply be the number in the middle of all the terms.

In this case, it is the number in red below

$12,12,44,44,44,66,67,{\color{Red} 67},78,99,107,123,143,367,578$

So our answer is 67.

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Example Question #39 : Median

A school district has determined that the most vaulable way to evaluate success is by using the median of all the test scores as the basis. With this in mind, find the median scores of 77, 80, 35, 76, 99, 95, 86, 65, 72, 56, and 21?

Possible Answers:

$\small 72$

$\small 76$

$\small 77$

$\small 65$

$\small 78$

Correct answer:

$\small 76$

Explanation:

The key to solving this problem is to first write the numbers in ascending order.

77, 80, 35, 76, 99, 95, 86, 65, 72, 56, 21

21, 35, 56, 65, 72, 76, 77, 80, 86, 95, 99

After this you will find the middle number of the set which turns out to be $\small 76$ .

21, 35, 56, 65, 72, 76, 77, 80, 86, 95, 99

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Example Question #40 : Median

What is the median of the function f(x)= x^2 -1 when (x=-6, -1, 0, 2, 4) ?

Possible Answers:

$\frac{25}{2}$

Correct answer:

Explanation:

We first plug each of the values into the function:

f(-6)=(-6)^2 - 1 = 35

f(-1)=(-1)^2 - 1 = 0

f(0)=(0)^2 - 1 = -1

f(2)=(2)^2 - 1 = 3

f(4)=(4)^2 - 1 = 15

Next, we put the answers in order from least to greatest:

-1, 0, 3, 15, 35

Now, to find the median, we find the value that is in the middle of the data set. Since our data set has an odd number of entries the median will be the value that have an equal number of values to either side of it. In this particular case that value lies at the third entry which is 3.

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Example Question #41 : Median

Find the median of the data set: [-3,9,10,-6]

Possible Answers:

$\frac{19}{2}$

$\frac{15}{2}$

$\frac{-9}{2}$

$\textup{There is no median.}$

Correct answer:

Explanation:

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

Reorder the data set from least to greatest.

$[-3,9,10,-6]\rightarrow[-6,-3,9,10]$

Since there are four numbers provided, the median is the average of the second and third numbers.

Average the two numbers.

$\frac{-3+9}{2} = \frac{6}{2}=3$

The median is:

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Example Question #42 : Median

Solve for the median: $[-\frac{1}{2}, -\frac{2}{5}, 3,-3]$

Possible Answers:

$\frac{9}{40}$

$\frac{13}{5}$

$-\frac{9}{20}$

$-\frac{9}{40}$

$-\frac{3}{10}$

Correct answer:

$-\frac{9}{20}$

Explanation:

Reorganize the data set in chronological order from least to greatest.

Negative half is less than negative two-fifth.

$[-\frac{1}{2}, -\frac{2}{5}, 3,-3] \rightarrow[-3,-\frac{1}{2}, -\frac{2}{5}, 3]$

Since this is an even number set of numbers, the median is the average of the middle two numbers.

Average the two fractions.

$\frac{-\frac{1}{2}+ (-\frac{2}{5})}{2} = \frac{-\frac{5}{10}-\frac{4}{10}}{2}= \frac{-\frac{9}{10}}{2}$

Rewrite the complex fraction using a division sign.

$\frac{-\frac{9}{10}}{2} = -\frac{9}{10} \div 2$

Change the division sign to multiplication and take the reciprocal of the second number.

$-\frac{9}{10} \times\frac{1}{2} = -\frac{9}{20}$

The median is: $-\frac{9}{20}$

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Example Question #43 : Median

Solve for the median: $[\frac{17}{3}, \frac{5}{2},\frac{3}{4}, \frac{1}{10}]$

Possible Answers:

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

$\frac{49}{12}$

$\frac{13}{8}$

$\frac{17}{40}$

$\frac{541}{240}$

Correct answer:

$\frac{13}{8}$

Explanation:

The median of an even number set is the average of the center two numbers in a chronological ordered set from least to greatest.

To arrange the data set, we will need to compare numerators of the similar denominator.

Find the least common denominator. The least common denominator is since it is the minimum number divisible by all of the existing denominators.

Convert all fractions to the common denominator.

$[\frac{17}{3}, \frac{5}{2},\frac{3}{4}, \frac{1}{10}]\rightarrow [\frac{17(20)}{3(20)}, \frac{5(30)}{2(30)},\frac{3(15)}{4(15)}, \frac{1(6)}{10(6)}]$

The data set becomes: $[\frac{340}{60}, \frac{150}{60}, \frac{45}{60}, \frac{6}{60}]$

We can now see that the middle two numbers are: $\frac{5}{2},\frac{3}{4}$

Average these two numbers.

$\frac{1}{2}[\frac{5}{2}+\frac{3}{4}] = \frac{1}{2}[\frac{10}{4}+\frac{3}{4}] =\frac{1}{2}[\frac{13}{4}]$

The answer is: $\frac{13}{8}$

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Example Question #44 : Median

Solve for the median: [9,9,1,1,9,1]

Possible Answers:

$\textup{There is no median.}$

Correct answer:

Explanation:

In order to solve for the median, we will need to rearrange the data set in chronological order from least to greatest.

$[9,9,1,1,9,1]\rightarrow[1,1,1,9,9,9]$

In an even set of data, the median is the average of the central two numbers.

Average the center two numbers.

$\frac{1+9}{2}= \frac{10}{2}=5$

The median is:

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Example Question #45 : Median

Solve for the median: $[\frac{2}{5},\frac{1}{2}, \frac{3}{8}, 1]$

Possible Answers:

$\frac{7}{16}$

$\textup{There is no median.}$

$\frac{9}{40}$

$\frac{7}{8}$

$\frac{9}{20}$

Correct answer:

$\frac{9}{20}$

Explanation:

The numbers not in chronological order.

Change the fractions and the integer to a common denominator. The common denominator of the fractions is since this is the least number that is divisible by each of the denominators given.

Convert the fractions.

$[\frac{2}{5},\frac{1}{2}, \frac{3}{8}, 1]\rightarrow [\frac{16}{40},\frac{20}{40},\frac{15}{40},\frac{40}{40}]$

The median of an even data set is the mean of the center two numbers in a chronological ordered data set from least to greatest.

$[\frac{15}{40},\frac{16}{40},\frac{20}{40},\frac{40}{40}]$

The central numbers are $\frac{16}{40}$ and $\frac{20}{40}$ .

Average these numbers.

$\frac{1}{2}(\frac{16}{40}+\frac{20}{40}) = \frac{1}{2}(\frac{36}{40}) = \frac{18}{40} =\frac{9}{20}$

The answer is: $\frac{9}{20}$

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Example Question #46 : Median

Solve for the median: $[\frac{2}{3}, 0, \frac{3}{4},1]$

Possible Answers:

$\frac{17}{24}$

$\frac{3}{8}$

$\frac{5}{6}$

$\frac{11}{24}$

$\frac{1}{2}$

Correct answer:

$\frac{17}{24}$

Explanation:

Reorder the data set from least to greatest.

$[\frac{2}{3}, 0, \frac{3}{4},1]\rightarrow [0,\frac{2}{3},\frac{3}{4},1]$

The median in an odd set of numbers will the average of the two central numbers given.

Average the two center numbers.

$\frac{1}{2}[\frac{2}{3}+\frac{3}{4}]=\frac{1}{2}[\frac{8}{12}+\frac{9}{12}] = \frac{1}{2}[\frac{17}{12}]$

The answer is: $\frac{17}{24}$

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Example Question #47 : Median

Determine the median: [1,3,2,9,8,7,5,35]

Possible Answers:

$\frac{35}{3}$

Correct answer:

Explanation:

The data set provided is not in chronological order.

Reorder the set from least to greatest.

$[1,3,2,9,8,7,5,35]\rightarrow[1,2,3,5,7,8,9,35]$

Since this an even numbered data set, we will need need to average the two center numbers to find the median.

$\frac{5+7}{2}=\frac{12}{2}=6$

The median is:

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Algebra II : Basic Statistics

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #38 : Median

Example Question #39 : Median

Example Question #40 : Median

Example Question #41 : Median

Example Question #42 : Median

Example Question #43 : Median

Example Question #44 : Median

Example Question #45 : Median

Example Question #46 : Median

Example Question #47 : Median

All Algebra II Resources

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