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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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Example Questions

Example Question #81 : Data Analysis And Probability

Find the mean of the following data set:

34,56,76,12,33,43,98,99,77,93,33

Possible Answers:

Correct answer:

Explanation:

Find the mean of the following data set:

34,56,76,12,33,43,98,99,77,93,33

For this question, the mean is essentially the same as the average.

Find the mean by adding up all our terms and dividing by the total number of terms.

$\mu=\frac{\sum }{n}$

In this case n=11 because we have 11 terms in our data set.

The sum can be found by adding our terms together.

$\mu=\frac{34+56+76+12+33+43+98+99+77+93+33}{11}$

$\mu=\frac{654}{11}=59.\bar{45}\approx 59$

So our mean is 59

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Example Question #82 : Data Analysis And Probability

Find the mean of the following data set:

17,43,44,50,59,67,78,78,81,94,99

Possible Answers:

Correct answer:

Explanation:

Find the mean of the following data set:

17,43,44,50,59,67,78,78,81,94,99

First, let's put our terms in ascending order.

17,43,44,50,59,67,78,78,81,94,99

Next, find the mean by adding up our terms and dividing by the total number of terms.

We have eleven terms, so our denominator will be eleven.

$\mu =\frac{17+43+44+50+59+67+78+78+81+94+99}{11}=\frac{710}{11}\approx65$

So our mean is 65

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Example Question #83 : Data Analysis And Probability

Use the following data set to answer the question:

4, 6, 8, 2, 3, 5, 2,7, 5,8

Find the mean.

Possible Answers:

Correct answer:

Explanation:

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

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

So, given the data set

4, 6, 8, 2, 3, 5, 2,7, 5,8

we will calculate the sum. To do that, we will add the numbers together. So,

$\text{sum of numbers in set} = 4+6+8+2+3+5+2+7+5+8$

$\text{sum of numbers in set} = 50$

Now, we will calculate the following:

$\text{number of numbers in set} = 10$

because if we count and see how many numbers are in the set, we get 10.

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

$\text{mean} = \frac{50}{10}$

$\text{mean} = 5$

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Example Question #84 : Data Analysis And Probability

If the mean of consecutive even numbers is , what is the smallest number of these ?

Possible Answers:

Correct answer:

Explanation:

Recall that the mean is the same as the average.

Let be the smallest number in this set. Since these are consecutive even numbers, the other numbers can be represented as $x+2, x+4, x+6, \text{ and }x+8$ .

Now, find the average of these numbers, and solve for .

$\text{Mean}=\frac{x+x+2+x+4+x+6+x+8}{5}=58$

5x+20=290

5x=270

x=54

The smallest number is .

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Example Question #85 : Data Analysis And Probability

A Math class took an exam. These were their scores:

90, 81, 98, 85,83, 92, 95, 77,82

Find the mean score.

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 following set of Math test scores

90, 81, 98, 85,83, 92, 95, 77,82

we can calculate the following:

$\text{sum of numbers within set} = 90+81+98+85+83+92+95+77+82$

$\text{sum of numbers within set} = 783$

Now, we will calculate the following:

$\text{number of numbers within set} = 9$

because there are 9 numbers in the set.

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

$\text{mean} = \frac{783}{9}$

$\text{mean} = 87$

Therefore, the mean score of the Math exams is 87.

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Example Question #31 : How To Find Mean

Find the mean of the following data set:

44,65,12,33,99,12,55,44,65,12,79

Possible Answers:

62.5

Correct answer:

Explanation:

Find the mean of the following data set:

44,65,12,33,99,12,55,44,65,12,79

Find the mean by first summing up our terms, then dividing by the number of terms we have.

In this case, we have 11 terms, so our denominator is 11

$\frac{44+65+12+33+99+12+55+44+65+12+79}{11}=\frac{521}{11}\approx47$

So, our mean is 47

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Example Question #32 : How To Find Mean

For his last six math tests, Josh scored 92, 80, 88, 94, 97, and 95. What is his mean test score?

Possible Answers:

95.5

Correct answer:

Explanation:

Recall that the mean is the same as the average.

To find the average, add up all the terms that are given and divide by the number of terms there are.

$\text{Mean}=\frac{\text{Sum of all terms}}{\text{Number of all terms}}$

$\text{Mean}=\frac{92+80+88+94+95+97}{6}=91$

His mean score is a .

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Example Question #641 : Isee Upper Level (Grades 9 12) Mathematics Achievement

In a class of students, a poll was taken to see how many siblings students had. The results in the poll were then made into a table.

Number of Siblings	Number of Students with the Specific Number of Siblings
0	5
1	9
2	4
3	2

What is the mean number of siblings for this class?

Possible Answers:

1.15

1.05

1.10

1.20

Correct answer:

1.15

Explanation:

Recall that the mean is another way of saying "average."

To find the average, we will need to find the total number of siblings the class has, then divide by the number of students in the class.

$\\ \text{Mean}=\frac{0+0+0+0+0+1+1+1+1+1+1+1+1+1+2+2+2+2+3+3}{20} \\\text{Mean}=\frac{23}{20}=1.15$

Thus, the mean number of siblings the class has is 1.15

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Example Question #642 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Michael received the following scores on his last four French tests: 65, 58, 69, 58.

If his mean test score must be a 70 in the class to pass, what must he score on his fifth test?

Possible Answers:

100

102

Correct answer:

100

Explanation:

Remember that the mean is the same as the average.

Let be the score he needs on his fifth test. Since we already know what his average needs to be, we can set up the following equation:

$\frac{65+58+69+58+x}{5}=70$

Solve for .

250+x=350

x=100

Michael must score 100 on his next test to pass.

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Example Question #643 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Over the course of seven games, Joanna scored the following number of points for her high school's varsity basketball team:

14, 20, 12, 9, 10, 8, 12

In order for her to be considered for the state-wide all-star team, she needs to have a mean score of 15 points per game for the entire season. If there is only one game left in the season, how many points must Joanna score in order to make it on to the all-star team?

Possible Answers:

Correct answer:

Explanation:

Recall that the mean is just the same as the average. Let be the number of points she must score in the last game. We can then write the following equation:

$\text{Mean}=\frac{14+20+12+9+10+8+12+x}{8}=15$

Now, solve for .

85+x=120

x=35

Joanna must score points in the next game to make the all-star team.

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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 #81 : Data Analysis And Probability

Example Question #82 : Data Analysis And Probability

Example Question #83 : Data Analysis And Probability

Example Question #84 : Data Analysis And Probability

Example Question #85 : Data Analysis And Probability

Example Question #31 : How To Find Mean

Example Question #32 : How To Find Mean

Example Question #641 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #642 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #643 : Isee Upper Level (Grades 9 12) Mathematics Achievement

All ISEE Upper Level Math Resources

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