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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

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Example Question #11 : How To Find Mean

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 #11 : How To Find Mean

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 points.

The mean goes down by 0.6 points.

The mean goes down by points.

The mean goes up by 0.6 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 #14 : How To Find 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: 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:

9.2

9.3

9.5

9.1

9.4

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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Example Question #21 : How To Find Mean

Consider the data set

$\left \{ 24,61, 27, 57, 34, 37, 63, 50, N\right \}$ .

For what value of does this set have a mean of ?

Possible Answers:

N = 97

N = 87

N = 47

N = 77

N = 57

Correct answer:

N = 97

Explanation:

The mean of a nine-element data set is the sum of the data elements divided by ; therefore,

$\frac{ N+ 24 + 61 + 27+ 57+ 34+ 37+ 63+ 50 }{9} = m$

$\frac{ N+ 353}{9} = 50$

$\frac{ N+ 353}{9} \cdot 9 = 50\cdot 9$

N+ 353 = 450

N+ 353 -353 = 450-353

N = 97

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Example Question #21 : Mean

What is the mean of the following numbers?

47,33,12,71,57

Possible Answers:

Correct answer:

Explanation:

The mean is equal to the sum of the values divided by the total number of values ().

$mean=\frac{\sum_n}{n}=\frac{47+33+12+71+57}{5}=\frac{220}{5}=44$

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Example Question #71 : Data Analysis And Probability

David's course score in a chemistry course is the mean of five tests. He has scored 72, 81, 79, and . What must he score on the fifth test to be assured of a course score of ?

Possible Answers:

Correct answer:

Explanation:

Let be the minimum fifth test score. Then the average of the scores is

$\frac{N + 72 + 81 + 79 + 85 }{5} = 80$ .

$\frac{N + 317 }{5} = 80$

$\frac{N + 317 }{5} \cdot 5 = 80 \cdot 5$

N + 317 = 400

N + 317 -317 = 400-317

N = 83 , the minimum score David needs.

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Example Question #22 : Mean

What is the median of the following set?

$\sqrt{17}, 4, \frac{8}{5}, 5, 2$

Possible Answers:

$\frac{8}{5}$

$\sqrt{17}$

Correct answer:

Explanation:

The median is the middle number in a set when the numbers are ordered from smallest to largest. The first step is to rearrange the numbers from smallest to largest.

$\frac{8}{5}, 2, 4,\sqrt{17}, 5$

Given that there are 5 items in this set, the median will be the third number (which is the middle number. That number is 4, the correct answer.

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Example Question #631 : Isee Upper Level (Grades 9 12) Mathematics Achievement

What is the mean of the set below?

$(2^{2}, 2^{3}, 2^{4}, 2^{5})$

Possible Answers:

Correct answer:

Explanation:

The first step to finding the mean is to convert the set to integers.

$(2^{2}, 2^{3}, 2^{4}, 2^{5})$

This simplifies to:

(4, 8, 16, 32)

The mean is determined by adding together the numbers in a set and then dividing by the total number of items in that set. This gives us:

$\frac{4+8+16+32}{4}=\frac{60}{4}=15$

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Example Question #23 : Mean

Find the mean of the following data set:

45,67,12,34,55,88,67,343,49

Possible Answers:

331

Correct answer:

Explanation:

Find the mean of the following data set:

45,67,12,34,55,88,67,343,49

To find the mean, we need to add up all our numbers, and then divide by the number of terms.

In this case, we have nine terms, so we will divide by nine.

$\mu=\frac{45+67+12+34+55+88+67+343+49}{9}=\frac{760}{9}\approx 84$

So, our answer is 84

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Example Question #27 : How To Find Mean

Find the mean of the following data set:

5,76,12,34,55,89,76,109,67,33,9

Possible Answers:

104

Correct answer:

Explanation:

Find the mean of the following data set:

5,76,12,34,55,89,76,109,67,33,9

Let's begin by rearranging our terms from least to greatest:

5,9,12,33,34,55,67,76,76,89,109

Next, we will sum up our terms and divide by the total number of terms. We have 11 terms, so our numerator will be 11.

$\mu =\frac{5+9+12+33+34+55+67+76+76+89+109}{11}$

$\mu=\frac{565}{11}=51.36\approx51$

So, our answer is 51.

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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 #11 : How To Find Mean

Example Question #11 : How To Find Mean

Example Question #14 : How To Find Mean

Example Question #21 : How To Find Mean

Example Question #21 : Mean

Example Question #71 : Data Analysis And Probability

Example Question #22 : Mean

Example Question #631 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #23 : Mean

Example Question #27 : How To Find Mean

All ISEE Upper Level Math Resources

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