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ISEE Upper Level Math : Data Analysis and Probability

Study concepts, example questions & explanations for ISEE Upper Level Math

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All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #644 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Use the following data set of test scores to answer the question:

99, 95, 84, 99, 81, 97, 79, 86

Find the mean.

Possible Answers:

Correct answer:

Explanation:

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

$\text{mean} = \frac{\text{sum of numbers within set}}{\text{number of numbers within set}}$

Now, given the set of test scores, we can calculate the following:

$\text{sum of numbers within set} = 99+95+84+99+81+97+79+86$

$\text{sum of numbers within set} = 720$

Now, we will calculate the following:

$\text{number of numbers within set} = 8$

because there are 8 numbers in the set.

Knowing all of this, we can substitute into the formula. We get

$\text{mean} = \frac{720}{8}$

$\text{mean} = 90$

Therefore, the mean score of the tests is 90.

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Example Question #91 : Data Analysis And Probability

The data set below represents a class's scores on a recent math test. What is the mode score in the data set?

$\small \left \{ 77,70,68,89,67,95,77,92,83,77,68,75\right \}$

Possible Answers:

73.1

Correct answer:

Explanation:

The mode is simply the value that appears most often in a given data set. In this data set the value 77 appears three times. The value 68 appears twice. No other value appears more than once, which means 77 is the mode.

You may want to arrange the values in numerical order if it helps you see the repeating values, but it isn't required.

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Example Question #2 : Mode

Examine the data set $\left \{ 1, 3, 8, 4, 7, 9, 10, 6, 2, N\right \}$ . You are given that can be any integer from 1 to 10.

Which value(s) of would give the data set no mode?

Possible Answers:

Only 5.

Any integer from 1 to 10 except 5.

1, 3, 5, 7, or 9.

This is impossible for any value of .

Any integer from 1 to 10.

Correct answer:

Only 5.

Explanation:

The mode of a data set is the element that appears most frequently; a data set with no mode has all of its elements appear exactly once.

All of the integers from 1 to 10 except for 5 are known to appear in this data set at least once. If is equal to any of those integers, it is the only one repeated, and it is the mode. Only if N = 5 can the set not have a repeated value. That makes this the correct choice.

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Example Question #1 : Mode

Give the mode(s) of the data set:

$\left \{ 1, 3, 4, 4, 5, 5, 6, 7, 7, 7, 8, 9, 10\right \}$

Possible Answers:

$4,5,\textrm{ and }7$

$5 \frac{1}{3}$

The data set has no mode.

Correct answer:

Explanation:

The mode of a data set is the element that appears most frequently. In this set, that element is , which appears three times. No other element appears more than twice.

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Example Question #1 : Mode

Give the mode(s) of the data set

$\left \{ 1, 3, 4, 5, 5, 5, 6, 7, 7, 7, 8, 9, 10\right \}$

Possible Answers:

$5 \textrm{ and }7$

The data set has no mode.

Correct answer:

$5 \textrm{ and }7$

Explanation:

The mode of a data set is the element that appears the most frequently. When two numbers both appear most frequently, there are two modes:

$5 \textrm{ and }7$

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Example Question #2 : Mode

Find the mode and the median of the frequency distribution shown in the following table:

$\begin{matrix} Data \ Value & Frequency \\ 77 & 7\\ 79& 3\\ 82& 4\\ 88& 1 \end{matrix}$

Possible Answers:

$Mode=78\ , Median=80$

$Mode=77\ , Median=78$

$Mode=82\ , Median=79$

$Mode=77\ , Median=79$

$Mode=78\ , Median=79$

Correct answer:

$Mode=77\ , Median=79$

Explanation:

The mode is the value that appears most often or has more frequency which is in this problem. The total number of data values are 7+3+4+1=15 . Since the number of values is odd, the median is the single middle value which is the 8th value in this problem. So the median is .

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Example Question #3 : Mode

in the following set of data the mode is 120 , what are the possible values for .

$\begin{matrix} Data \ Value & Frequency \\ 80& 18\\ 90& 22\\ 110& 12\\ 120& x\\ 140& 11 \end{matrix}$

Possible Answers:

x<22

x>18

x>12

x<20

x>22

Correct answer:

x>22

Explanation:

The mode is the value that has more frequency in a given set of data than other values. Among the given frequencies in this problem, has the frequency of which is more than others. If 120 is the mode, its frequency must be more than .

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Example Question #4 : Mode

The heights of the starting volleyball team for a high school are $68,74,77,80,82,83\ and \ 80$ inches. Give the mode of this data set.

Possible Answers:

$68\ in$

$77\ in$

$80\ in$

$82\ in$

$83\ in$

Correct answer:

$80\ in$

Explanation:

The mode is the value that appears most often which is $80\ in$ in this data set, because $80\ in$ appears two times while all of the other values only appear one time.

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Example Question #92 : Data Analysis And Probability

In the following set of scores find the mode:

$\begin{matrix} Data \ Value & Frequency \\ 80& 12\\ 74& 14\\ 85& 7\\ 82& 8\\ 64& 11 \end{matrix}$

Possible Answers:

Correct answer:

Explanation:

The mode is the value that appears most often or has more frequency in a given set of data. So in this problem, the mode is which occurs most frequently.

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Example Question #8 : Mode

Consider the data set $\left \{ 2, 4, 4, 4, 6, 6, 6, 7, 8, 10, N, N\right \}$ . If the data set has only one mode, how many possible values of are there?

Possible Answers:

Infinitely many

Correct answer:

Explanation:

If $N \in \left \{ 4,6\right \}$ then the value of is appears five times, more than any other element. This would give the set one mode.

If $N \in \left \{ 2,7,8,10\right \}$ , then 4, 6, and the value of would appear three times each, more than any other element. This would give the set three modes.

If assumes any other value, then 4 and 6 would appear three times each, more than any other element. This would give the set two modes.

Therefore, there are only two values of that would give the set one mode.

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : Data Analysis and Probability

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #644 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #91 : Data Analysis And Probability

Example Question #2 : Mode

Example Question #1 : Mode

Example Question #1 : Mode

Example Question #2 : Mode

Example Question #3 : Mode

Example Question #4 : Mode

Example Question #92 : Data Analysis And Probability

Example Question #8 : Mode

All ISEE Upper Level Math Resources

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