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Algebra II : Basic Statistics

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Example Questions

Example Question #25 : Mode

For the function f(x)= x^2 + x +2 , what is the mode if $x = \left \{ -3, -1, 0, 1, 3\right \}$ ?

Possible Answers:

Correct answer:

Explanation:

In order to find the mode, first we need to evaluate the function at each of our points:

f(-3)= (-3)^2 + (-3) +2 = 8

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

f(0)= (0)^2 + (0) +2 = 2

f(1)= (1)^2 + (1) +2 = 4

f(3)= (3)^2 + (3) +2 = 14

Now we put our answers in order:

2, 2, 4, 8, 14

As we can see, the appears twice, which is more than any other number. Therefore the mode is .

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Example Question #25 : Mode

Find the mode of the data: {1,8,5,4,7,5,6,3,6,4,7,5,7,5}

Possible Answers:

5.21

Correct answer:

Explanation:

The mode is the data point that occurs most in the set. Grouping the data shows the 5 is the data point that occurs the most. {1,3,4,4,5,5,5,5,6,6,7,7,7,8}

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Example Question #27 : Mode

What is the mode(s) of:

8,2,9,4,5,5,6,6,7,7,7,8,6 ?

Possible Answers:

7,6

Correct answer:

7,6

Explanation:

Step 1: Arrange the numbers from smallest to largest:

2,4,5,5,6,6,6,7,7,7,8,8,9

Step 2: Compare the number of times that each number appears

2-1 time
4-1 time
5-2 times
6-3 times
7-3 times
8-2 times
9-1 time

Step 3: We see that two numbers appear more often than others. Both of those numbers are the modes of the set.

The modes are and .

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Example Question #342 : Basic Statistics

Calculate the mode: $[\frac{1}{2}, 0.5, 50\%, 1,1, 1,30]$

Possible Answers:

$\textup{There is no mode.}$

$\frac{3}{4}$

$\frac{69}{14}$

0.5,1

Correct answer:

0.5,1

Explanation:

Convert the fraction and percent to a decimal.

$[\frac{1}{2}, 0.5, 50\%, 1,1, 1,30]\rightarrow [0.5,0.5,0.5,1,1,1,30]$

The mode is the number or numbers that has the highest frequency in a data set.

The highest frequencies of numbers are 0.5,1 , since occurs only once.

This means that the mode is: 0.5,1

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Example Question #312 : Data Properties

Determine the mode: $[\frac{1}{2}, 5\%, 50\%, \sqrt4, \frac{1}{20}]$

Possible Answers:

$\frac{1}{2}$

$\frac{1}{2},\frac{1}{20}$

$\textup{There is no mode.}$

$\frac{1}{20}$

Correct answer:

$\frac{1}{2},\frac{1}{20}$

Explanation:

The mode is the number or numbers that have the highest frequency in the data set.

Convert all numbers to a common number. Change all to decimal.

$[\frac{1}{2}, 5\%, 50\%, \sqrt4, \frac{1}{20}]\rightarrow [0.5,0.05,0.5,2,0.05]$

Notice that the numbers 0.5, 0.05 occurs twice in the data set, while occurs only once in the data set.

The mode is: $\frac{1}{2},\frac{1}{20}$

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Example Question #31 : Mode

Find the mode: [1,9,18,9,23,0]

Possible Answers:

$\frac{17}{2}$

$\textup{There is no mode.}$

Correct answer:

Explanation:

The mode is the number or numbers with the highest frequency in the data set.

It is not necessary to reorganize the set of data in chronological order.

The only number that appears more than once is the integer .

All of the other numbers appear only once in the data set.

Therefore, the mode of this data set is:

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Example Question #341 : Basic Statistics

Determine the mode: [0,1,2,3,4,6,8,100]

Possible Answers:

100

$\frac{7}{2}$

$\textup{No mode.}$

$\frac{31}{4}$

$\textup{All the numbers given.}$

Correct answer:

$\textup{No mode.}$

Explanation:

The mode is defined as the number or numbers that have the highest frequency in a set of data.

Each number given in the data set has only one frequency.

This means that there is no mode.

The answer is: $\textup{No mode.}$

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Example Question #32 : Mode

Determine the mode: [1,6,4,8,9,4,1]

Possible Answers:

1,4

Correct answer:

1,4

Explanation:

The mode is defined to be the number or numbers with the highest frequency in the data set.

Every number except one and four have frequencies of 1.

The numbers one and four appear twice in the set of data.

The mode is: 1,4

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Example Question #33 : Mode

Determine the mode of the set of numbers: [5,9,6,10,6,10,9,3]

Possible Answers:

3,5

$\frac{15}{2}$

$\frac{29}{4}$

$\textup{There is no mode.}$

6,9,10

Correct answer:

6,9,10

Explanation:

Identify the highest occurrence of the numbers in the data set. The mode includes all numbers that has the highest frequency that occurs in the data.

The values six, nine, and ten, occurs twice, while three and five occurs only once.

The mode is: 6,9,10

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Example Question #34 : Mode

Determine the mode of the set of data: [4,-4,9,9,-4,1,10]

Possible Answers:

$\frac{25}{7}$

$\frac{5}{2}$

$\textup{There is no mode.}$

-4,9

Correct answer:

-4,9

Explanation:

The mode is the number or numbers that have the highest occurrence in the set of data.

The numbers nine and negative four occurs twice, and the other numbers occur only one. Do not mix the definition of mode with mean and median.

The answer is: -4,9

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Algebra II : Basic Statistics

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #25 : Mode

Example Question #25 : Mode

Example Question #27 : Mode

Example Question #342 : Basic Statistics

Example Question #312 : Data Properties

Example Question #31 : Mode

Example Question #341 : Basic Statistics

Example Question #32 : Mode

Example Question #33 : Mode

Example Question #34 : Mode

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