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ISEE Upper Level Math : Mean

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Example Questions

Example Question #11 : Mean

The heights of a football team's members are $\displaystyle 68,70,75,72,73$ and $\displaystyle 78$ inches. Find the mean of the heights.

Possible Answers:

$\displaystyle 74,667in$

74in $\displaystyle 74in$

$\displaystyle 72.667in$

73in $\displaystyle 73in$

$\displaystyle 73.667in$

Correct answer:

$\displaystyle 72.667in$

Explanation:

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

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

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Example Question #62 : Data Analysis And Probability

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

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

Possible Answers:

79.5 $\displaystyle 79.5$

$\displaystyle 80$

$\displaystyle 79$

$\displaystyle 78$

$\displaystyle 82$

Correct answer:

$\displaystyle 79$

Explanation:

The mean of the scores can be calculated as:

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

Where:

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

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

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Example Question #64 : Data Analysis

The mean of five numbers is $\displaystyle 32$. Give their sum.

Possible Answers:

180 $\displaystyle 180$

160 $\displaystyle 160$

150 $\displaystyle 150$

200 $\displaystyle 200$

240 $\displaystyle 240$

Correct answer:

160 $\displaystyle 160$

Explanation:

The mean of five numbers is equal to their sum divided by $\displaystyle 5$, or as a formula we can write:

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

Where:

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

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Example Question #12 : How To Find Mean

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

Possible Answers:

8t+2 $\displaystyle 8t+2$

t+4 $\displaystyle t+4$

t+2 $\displaystyle t+2$

t-2 $\displaystyle t-2$

8t+4 $\displaystyle 8t+4$

Correct answer:

t+2 $\displaystyle t+2$

Explanation:

The mean of eight numbers is equal to their sum divided by $\displaystyle 8$ or as a formula we can write:

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

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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 $\displaystyle t$.

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

Possible Answers:

2t+2 $\displaystyle 2t+2$

4t+4 $\displaystyle 4t+4$

8t+8 $\displaystyle 8t+8$

t+1 $\displaystyle t+1$

t+2 $\displaystyle t+2$

Correct answer:

t+1 $\displaystyle t+1$

Explanation:

The mean of the scores can be calculated as:

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

Where:

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

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

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

$\displaystyle =t+1$

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

The sum of a set of values is $\displaystyle 72$. If the mean of the data set is $\displaystyle 12$, give the number of values in the set.

Possible Answers:

$\displaystyle 6$

$\displaystyle 5$

$\displaystyle 8$

$\displaystyle 4$

$\displaystyle 7$

Correct answer:

$\displaystyle 6$

Explanation:

Mean of the scores can be calculated as:

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

Where:

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

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

The mean of $\displaystyle 14$ test scores is $\displaystyle 75$. When the 15th $\displaystyle 15th$ student takes the test, the mean goes down by two points. Give the 15th $\displaystyle 15th$ score.

Possible Answers:

$\displaystyle 70$

$\displaystyle 75$

$\displaystyle 50$

$\displaystyle 40$

$\displaystyle 45$

Correct answer:

$\displaystyle 45$

Explanation:

The total of $\displaystyle 14$ test scores is $14\times 75=1050$ $\displaystyle 14\times 75=1050$. The mean of the total scores for $\displaystyle 15$ students would be:

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

Where:

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

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

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

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

$\Rightarrow x_{15}=45$ $\displaystyle \Rightarrow x_{15}=45$

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Example Question #71 : Data Analysis And Probability

The sum of $\displaystyle 10$ test scores is 770 $\displaystyle 770$. When the 11th $\displaystyle 11th$ student takes the test, the mean of the scores does not change. Give the score of the 11th $\displaystyle 11th$ student.

Possible Answers:

$\displaystyle 75$

$\displaystyle 77$

$\displaystyle 79$

$\displaystyle 80$

$\displaystyle 78$

Correct answer:

$\displaystyle 77$

Explanation:

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

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

Where:

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

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

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

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

$\Rightarrow x=847-770=77$ $\displaystyle \Rightarrow x=847-770=77$

That means the 11th $\displaystyle 11th$ student should get the score of $\displaystyle 77$ 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 $\displaystyle 19$ test scores is 1558 $\displaystyle 1558$. When the 20th $\displaystyle 20th$ student takes the test and gets a score of $\displaystyle 70$, how does the mean change?

Possible Answers:

The mean goes up by 0.6 $\displaystyle 0.6$ points.

The mean goes down by 0.6 $\displaystyle 0.6$ points.

The mean goes down by $\displaystyle 1$ points.

The mean goes up by $\displaystyle 1$ points.

The mean goes down by $\displaystyle 2$ points.

Correct answer:

The mean goes down by 0.6 $\displaystyle 0.6$ points.

Explanation:

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

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

Where:

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

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

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

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Example Question #12 : Mean

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: $\displaystyle 9.2, 9.5, 9.6, 9.7, 9.5, 9.0, 8.7$. What is Donna's score, rounded to the nearest tenth?

Possible Answers:

9.4 $\displaystyle 9.4$

9.2 $\displaystyle 9.2$

9.1 $\displaystyle 9.1$

9.3 $\displaystyle 9.3$

9.5 $\displaystyle 9.5$

Correct answer:

9.4 $\displaystyle 9.4$

Explanation:

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

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

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : Mean

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #11 : Mean

Example Question #62 : Data Analysis And Probability

Example Question #64 : Data Analysis

Example Question #12 : How To Find Mean

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 #12 : Mean

All ISEE Upper Level Math Resources

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