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ISEE Upper Level Math : How to find mean

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Example Questions

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:

74,667in

74in

73.667in

72.667in

73in

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 #63 : Data Analysis

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 #64 : Data Analysis

The mean of five numbers is . Give their sum.

Possible Answers:

180

160

150

200

240

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 #65 : Data Analysis

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

Possible Answers:

t+2

8t+4

8t+2

t-2

t+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

4t+4

8t+8

t+1

t+2

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

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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Example Question #71 : Data Analysis And Probability

The sum of test scores is 770 . When the 11th student takes the test, the mean of the scores does not change. Give the score of the 11th student.

Possible Answers:

Correct answer:

Explanation:

The mean is the sum of the data values divided by the number of values or as a formula we have:

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

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 have:

$\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}=\frac{770}{10}=77$

When the 11th student takes the test the mean of the score does not change. Let:

x=11th student score. So we can write:

$New\ Mean=77=\frac{770+x}{11}\Rightarrow 770+x=77\times 11$

$\Rightarrow x=847-770=77$

That means the 11th student should get the score of which is equal to the initial mean in order to get the same value for the new mean.

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

The sum of test scores is 1558 . When the 20th student takes the test and gets a score of , how does the mean change?

Possible Answers:

The mean goes up by 0.6 points.

The mean goes down by 0.6 points.

The mean goes down by points.

The mean goes up by points.

The mean goes down by points.

Correct answer:

The mean goes down by 0.6 points.

Explanation:

The mean is the sum of the data values divided by the number of values or as a formula we have:

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

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. The total of test scores is 1558 ; the mean of the scores is:

$\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}=\frac{1558}{19}=82$

When the 20th student takes the test the sum of scores would be 1558+70=1628 and the new mean of the scores is:

$\bar{x_{1}}=\frac{1}{n}\sum_{i=1}^{n}x_{i}=\frac{1628}{20}=81.4$

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Example Question #623 : Isee Upper Level (Grades 9 12) Mathematics Achievement

A gymnastics meet has seven judges. After each routine, each judge assigns a merit-based score from 0 to 10; a contestant's score for the routine is the mean of all the judges' scores except for the highest and the lowest.

The seven judges individually assigned the following scores to one of Donna's routines: 9.2, 9.5, 9.6, 9.7, 9.5, 9.0, 8.7 . What is Donna's score, rounded to the nearest tenth?

Possible Answers:

9.4

9.3

9.5

9.1

9.2

Correct answer:

9.4

Explanation:

The highest and lowest scores, 9.7 and 8.7 , are tossed out, so Donna's score is the mean of the five that remain.

$\frac{ 9.2+ 9.5+9.6+ 9.5+ 9.0 }{5} = \frac{ 46.8 }{5} = 9.36 \approx 9.4$

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ISEE Upper Level Math : How to find mean

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #61 : Data Analysis And Probability

Example Question #63 : Data Analysis

Example Question #64 : Data Analysis

Example Question #65 : Data Analysis

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

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

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

Example Question #71 : Data Analysis And Probability

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

Example Question #623 : Isee Upper Level (Grades 9 12) Mathematics Achievement

All ISEE Upper Level Math Resources

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