ISEE Middle Level Quantitative : ISEE Middle Level (grades 7-8) Quantitative Reasoning

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

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Example Questions

Example Question #2 : How To Find Mean

The six students in the science club weigh 145 pounds, 172 pounds, 166 pounds, 159 pounds, 153 pounds, and 201 pounds. Find the mean of their weights.

Possible Answers:

\displaystyle 173\textrm{ lbs}

\displaystyle 166\textrm{ lbs}

\displaystyle \textrm{160 lbs}

\displaystyle 153 \textrm{ lbs}

\displaystyle 162.5 \textrm{ lbs}

Correct answer:

\displaystyle 166\textrm{ lbs}

Explanation:

Add the weights, then divide the sum by six:

\displaystyle 145+172+166+159+153+201=996

\displaystyle 996 \div 6 = 166

Example Question #3 : How To Find Mean

Give the mean of the data set \displaystyle \left \{ 2, 4, 8, 16, 32, 64\right \}

Possible Answers:

\displaystyle 12

\displaystyle 16

\displaystyle 8

\displaystyle 21

\displaystyle 33

Correct answer:

\displaystyle 21

Explanation:

There are six elements, so to find the mean, add the elements and divide by six:

\displaystyle \left ( 2+4+8+16+32+64 \right )\div 6 = 126 \div 6 = 21

Example Question #1 : How To Find Mean

The mean of the weights of the eleven students in the math club is 186 pounds. Which is the greater quantity?

(A) The sum of the weights of the students

(B) One ton 

Possible Answers:

(B) is greater

(A) and (B) are equal

It is impossible to determine which is greater from the information given

(A) is greater

Correct answer:

(A) is greater

Explanation:

One ton is equal to 2,000 pounds.

The mean of the weights of the students is the total of their weights divided by the number of students.

Let \displaystyle T be the total of their weights.

\displaystyle 186 = T \div 11

\displaystyle T = 186 \cdot11 = 2,046 > 2,000

(A) is greater.

 

Example Question #281 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

David scored 77, 92, and 80 on his first 3 tests. He currently has a test score average of 83. What grade would David need on the next test to increase his test score average to 85?

Possible Answers:

\displaystyle 94

\displaystyle 82

\displaystyle 85

\displaystyle 91

\displaystyle 99

Correct answer:

\displaystyle 91

Explanation:

You can find the average of a set of numbers by adding up the numbers and dividing by how many numbers are in the data set. Since David is trying to acheive an average of 85 by his fourth test, we should multiply 85 by 4.

\displaystyle \text{average}=85=\frac{\text{total}}{4}

\displaystyle \text{total}=85\times4 = 340

The result is the number that the four tests should total in order to achieve an average of 85. Then, add up the test scores Daid has recieved so far:

\displaystyle 77 + 92 + 80 = 249

If you subtract this number (the total from the test scores so far) from 340, the result will be the score needed to achieve the 85 average.

\displaystyle 340 - 249 = 91

David must score a 91 on his fourth test.

Example Question #4 : How To Find Mean

June ran 2 miles Monday, 3 miles Tuesday, 3 miles Thursday, and 2 miles Friday. How many miles did June run on average from Monday to Friday?

Possible Answers:

\displaystyle 1

\displaystyle 2

\displaystyle 2.25

\displaystyle 3

\displaystyle 2.5

Correct answer:

\displaystyle 2

Explanation:

You can find the average of a set of numbers by adding up all the numbers in that set and dividing by how many numbers you added total. Here is a summary of our set:

Monday: 2 miles

Tuesday: 3 miles

Wednesday: 0 miles

Thursday: 3 miles

Friday: 2 miles

Keep in mind that we are looking for the average number of miles June ran Monday through Friday, and that there are 5 days in that period. You must also account for the 0 miles that June ran on Wednesday. 

\displaystyle \text{average}=\frac{\text{total miles}}{\text{total days}}=\frac{2+3+0+3+2}{5}=\frac{10}{5}

June ran a total of 10 miles during that 5 day period. You must then divide by the number of days in order to get the average.

\displaystyle 10 \div 5 = 2

Example Question #81 : Statistics & Probability

In a group of 4 books, the average number of pages is is 10.  Juan adds a book with 20 pages to the group.  What is the new average number of pages?

Possible Answers:

\displaystyle 30

\displaystyle 20

\displaystyle 12

\displaystyle 15

\displaystyle 10

Correct answer:

\displaystyle 12

Explanation:

If the average of 4 books was 10, then the total number of pages was \displaystyle 4\times10 =40. Adding in the 20 new pages, but now dividing by 5 you get \displaystyle 60/5 = 12.

Example Question #1 : Mean

Give the mean of the data set (nearest tenth, if applicable): 

\displaystyle \left \{ 56,78,98,85,77,73 \right \}

Possible Answers:

\displaystyle 77.8

\displaystyle 75.7

\displaystyle 76.5

\displaystyle 77.3

\displaystyle 79.6

Correct answer:

\displaystyle 77.8

Explanation:

Add the six elements and divide the sum by 6:

\displaystyle 56 + 78 + 98 + 85 +77 + 73 = 467

\displaystyle 467 \div 6 \approx 77.8

Example Question #82 : Statistics & Probability

Find the mean of this set of numbers:

54, 41, 99, 120, 66.

Possible Answers:

\displaystyle 80

\displaystyle 79

\displaystyle 99

\displaystyle 76

Correct answer:

\displaystyle 76

Explanation:

Firrst, add the numbers:

\displaystyle 54+41+99+120+66=380

Then, divide by the amount of numbers in the set:

\displaystyle 380\div 5=76

Answer: The mean is 76.

Example Question #1 : Mean

Give the mean of the following eight scores: 

\displaystyle \left \{ 61, 67, 80, 72, 76, 73, 90, 68 \right \}

Possible Answers:

\displaystyle 72.5

\displaystyle 72.875

\displaystyle 73.375

\displaystyle 75.5

\displaystyle 73

Correct answer:

\displaystyle 73.375

Explanation:

Divide the sum of the scores by eight:

\displaystyle \frac{ 61+ 67+80+72+76+73+90+ 68}{8} = \frac{ 587}{8} = 73.375

Example Question #1 : Find Mean

Give the mean of the following nine scores: 

\displaystyle \left \{ 61, 67, 80, 72, 76, 73, 90, 68, 70 \right \}

Possible Answers:

\displaystyle 73

\displaystyle 72.5

\displaystyle 72

\displaystyle 68

\displaystyle 75.5

Correct answer:

\displaystyle 73

Explanation:

Divide the sum of the scores by nine:

\displaystyle \frac{ 61 + 67+ 80+ 72+ 76+73+90+68+70}{9} = \frac{ 657}{9} = 73

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