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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 #2 : How To Find Mean

The mean of the following numbers is . Solve for .

17, 14, 22, 11, 14, 16, n

Possible Answers:

n=12

n=14

n=13

n=11

Correct answer:

n=11

Explanation:

The mean is determined by dividing the sum of the values by the total number of values:

$mean=\frac{17+14+22+11+14+16+n}{7}=15$

17+14+22+11+14+16+n=105

94+n=105

n=11

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Example Question #8 : How To Find Mean

What is the mean of the first ten prime numbers?

Possible Answers:

12.1

13.1

15.8

10.1

12.9

Correct answer:

12.9

Explanation:

The first ten primes form the data set:

$\left \{ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29\right \}$

Add them, and divide by :

$\left ( 2 + 3+5+ 7+ 11+13+17+19+ 23+29 \right )\div 10 = 129\div 10= 12.9$

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Example Question #9 : How To Find Mean

Consider the following set of scores from a math test. If the mean is , give .

$\left \{ 80,75,74,70,90,84,t \right \}$

Possible Answers:

400

431

Correct answer:

Explanation:

Mean of the scores can be calculated as:

$\bar{x}=\frac{1}{n}\sum_{i=1}^n{x_{i}$

Where:

$\bar{x}$ is the mean of a data set, $\sum_{}^{}$ indicates the sum of the data values $x_{i}$ , and is the number of data values. So we can write:

$\bar{x}=\frac{1}{n}\sum_{i=1}^n{x_{i}$

$\Rightarrow 6=\frac{80+75+74+70+90+84+t}{7}$

$\Rightarrow 6=\frac{473+t}{7}\Rightarrow 473+t=6\times 7$

$\Rightarrow t=42-473=-431$

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Example Question #61 : Data Analysis And Probability

The heights of a football team's members are 68,70,75,72,73 and inches. Find the mean of the heights.

Possible Answers:

73in

74,667in

73.667in

74in

72.667in

Correct answer:

72.667in

Explanation:

The mean is the sum of all the data values divided by the number of values. So we can write:

$Mean=\frac{68+70+75+72+73+78}{6}\approx 72.667 in$

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Example Question #615 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Consider the following set of scores from a physics test. Give the mean of the scores.

$\left \{ 75,73,84,81,68,95,77 \right \}$

Possible Answers:

79.5

Correct answer:

Explanation:

The mean of the scores can be calculated as:

$\bar{x}=\frac{1}{n}\sum_{i=1}^n{x_{i}$

Where:

$\bar{x}$ is the mean of a data set, $\sum_{}^{}$ indicates the sum of the data values $x_{i}$ , and is the number of data values. So we can write:

$\bar{x}=\frac{1}{n}\sum_{i=1}^n{x_{i}=\frac{75+73+84+81+68+95+77}{7}=\frac{553}{7}=79$

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Example Question #616 : Isee Upper Level (Grades 9 12) Mathematics Achievement

The mean of five numbers is . Give their sum.

Possible Answers:

240

200

180

150

160

Correct answer:

160

Explanation:

The mean of five numbers is equal to their sum divided by , or as a formula we can write:

$\bar{x}=\frac{1}{n}\sum_{i=1}^n{x_{i}$

Where:

$\bar{x}$ is the mean of a data set, $\sum_{}^{}$ indicates the sum of the data values $x_{i}$ , and is the number of data values. So we can write:

$\sum_{i=1}^n{x_{i}=n\bar{x}\Rightarrow \sum_{i=1}^n{x_{i}=5\times 32=160$

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Example Question #617 : Isee Upper Level (Grades 9 12) Mathematics Achievement

The sum of numbers is 8t+16 . Find the mean in terms of . ( is a real number)

Possible Answers:

t+4

8t+2

t-2

t+2

8t+4

Correct answer:

t+2

Explanation:

The mean of eight numbers is equal to their sum divided by or as a formula we can write:

$\bar{x}=\frac{1}{n}\sum_{i=1}^n{x_{i}\Rightarrow \frac{8t+16}{8}=\frac{8(t+2)}{8}=t+2$

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Example Question #621 : Isee Upper Level (Grades 9 12) Mathematics Achievement

In the following set, find the mean in terms of .

$\left \{ t^2-1,t,t^2,2t,1-t^2,-t^2,7t,8-2t \right \}$

Possible Answers:

2t+2

t+2

8t+8

4t+4

t+1

Correct answer:

t+1

Explanation:

The mean of the scores can be calculated as:

$\bar{x}=\frac{1}{n}\sum_{i=1}^n{x_{i}$

Where:

$\bar{x}$ is the mean of a data set, $\sum_{}^{}$ indicates the sum of the data values $x_{i}$ , and is the number of data values. So we can write:

$\bar{x}=\frac{1}{n}\sum_{i=1}^n{x_{i}=\frac{t^2-1+t+t^2+2t+1-t^2-t^2+7t+8-2t}{8}$

$=\frac{(t^2+t^2-t^2-t^2)+(t^2+2t+7t-2t)+(-1+1+8)}{8}$

$=\frac{0+8t+8}{8}=\frac{8(t+1)}{8}$

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Example Question #622 : Isee Upper Level (Grades 9 12) Mathematics Achievement

The sum of a set of values is . If the mean of the data set is , give the number of values in the set.

Possible Answers:

Correct answer:

Explanation:

Mean of the scores can be calculated as:

$\bar{x}=\frac{1}{n}\sum_{i=1}^n{x_{i}$

Where:

$\bar{x}$ is the mean of a data set, $\sum_{}^{}$ indicates the sum of the data values $x_{i}$ , and is the number of data values. So we can write:

$\bar{x}=\frac{1}{n}\sum_{i=1}^n{x_{i}\Rightarrow n=\frac{1}{\bar{x}}\sum_{i=1}^n{x_{i}=\frac{72}{12}=6$

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Example Question #13 : How To Find Mean

The mean of test scores is . When the 15th student takes the test, the mean goes down by two points. Give the 15th score.

Possible Answers:

Correct answer:

Explanation:

The total of test scores is $14\times 75=1050$ . The mean of the total scores for students would be:

$\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}$

Where:

$\bar{x}$ is the mean of a data set, $\sum$ indicates the sum of the data values $x_{i}$ and is the number of data values. So we can write:

$\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}=\frac{1050+x_{15}}{15}=75-2$

$\Rightarrow 1050+x_{15}=73\times 15$

$\Rightarrow x_{15}=1095-1050$

$\Rightarrow x_{15}=45$

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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 #2 : How To Find Mean

Example Question #8 : How To Find Mean

Example Question #9 : How To Find Mean

Example Question #61 : Data Analysis And Probability

Example Question #615 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #616 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #617 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #621 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #622 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #13 : How To Find Mean

All ISEE Upper Level Math Resources

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