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SSAT Middle Level Math : How to find mean

Study concepts, example questions & explanations for SSAT Middle Level Math

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Example Questions

Example Question #91 : How To Find Mean

In Maria's family, her parents are both 45 years old, and her younger brother is 2 years younger than she is. What is the mean of their ages, if Maria is 5 years old?

Possible Answers:

$\displaystyle 24$

25.5 $\displaystyle 25.5$

$\displaystyle 25$

24.5 $\displaystyle 24.5$

Correct answer:

24.5 $\displaystyle 24.5$

Explanation:

The mean of a set is found by finding the sum of the set and then dividing by the number of items in the set. Given that both of her parents are 45 years old, that Maria is 5 years old, and that her brother is 3 years old (being 2 years younger than she is), the mean is calculated using this equation:

$\frac{45+45+5+3}{4}=24.5$ $\displaystyle \frac{45+45+5+3}{4}=24.5$

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Example Question #465 : Data Analysis And Probability

The substitute teacher gave her class a quiz. Initially, she believed that there were 15 students in her class who scored an average of 7 out of 10. However, she later realized that there was a 16th student in the class who simply refused to take the quiz, and thereby got a score of 0. What is the average quiz score (to the nearest hundredth), when considering this 16th student?

Possible Answers:

$\displaystyle 7$

6.65 $\displaystyle 6.65$

$\displaystyle 6$

6.56 $\displaystyle 6.56$

Correct answer:

6.56 $\displaystyle 6.56$

Explanation:

If 15 students got an average score of 7, and 1 student got a score of 0, the average score of the 16 students can be found with this equation:

$Average = \frac{15\cdot7+0}{16}$ $\displaystyle Average = \frac{15\cdot7+0}{16}$

$Average = \frac{105}{16}$ $\displaystyle Average = \frac{105}{16}$

$\displaystyle Average = 6.56$

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Example Question #91 : Mean

A student wishes to receive an average score of 92 percent in his history class. His grade consists of five test scores, the first four of which he received the following grades: 86, 97, 95, and 89. On the last test he receives an 88. Is this score enough to have the desired average in the class (assuming no rounding)? If no, then what score did he need?

Possible Answers:

No, he needs a 99 to have an average score of 92.

No, he needs a 92 to have an average score of 92.

No, he needs a 93 to have an average score of 92.

No, he needs a 89 to have an average score of 92.

Yes, this score will give him an average of 92.

Correct answer:

No, he needs a 93 to have an average score of 92.

Explanation:

The question asks to find the average score of the five tests taken and to compare it to the desired average of 92 percent. To find the average, add all five scores then divide by five.

$\frac{(86+97+95+89+x)}{5}=92$ $\displaystyle \frac{(86+97+95+89+x)}{5}=92$

His test score of 88 will give him a class average of 91, not 92. To determine what score he needs, take the final test score to be the variable x, and use the average equation again, this time using the desired average of 92. Solve for x.

$\frac{(86+97+95+89+88)}{5}=91$ $\displaystyle \frac{(86+97+95+89+88)}{5}=91$
$\displaystyle (86+97+95+89+x)=460$
$\displaystyle (367+x)=460$
$\displaystyle x=93$

Therefore, the score he must receive to average a 92, without rounding, is a 93.

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Example Question #111 : Data Analysis And Probability

What number is halfway between $\displaystyle 11$ and $\displaystyle 19$ ?

Possible Answers:

$\displaystyle 14$

$\displaystyle 15$

$16\tfrac{1}{2}$ $\displaystyle 16\tfrac{1}{2}$

$\displaystyle 17$

$\displaystyle 12$

Correct answer:

$\displaystyle 15$

Explanation:

The two numbers are $\displaystyle 8$ apart, so the number half way between is $\displaystyle 4$ away from both. Or you could find the average of $\displaystyle 11$ and $\displaystyle 19$ . The answer is the same.

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Example Question #91 : Mean

Find the mean of the following set of numbers: $\displaystyle 188, 199, 204, 173, 166$

Possible Answers:

186 $\displaystyle 186$

188 $\displaystyle 188$

185 $\displaystyle 185$

199 $\displaystyle 199$

173 $\displaystyle 173$

Correct answer:

186 $\displaystyle 186$

Explanation:

Add the numbers, and divide by 5:

$\frac{ 188+199+ 204+173+166}{5} = \frac{930}{5} =186$ $\displaystyle \frac{ 188+199+ 204+173+166}{5} = \frac{930}{5} =186$

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Example Question #92 : How To Find Mean

Find the mean of this set of numbers:

$\displaystyle 3257, 1254, 7485, 8960$

Possible Answers:

7706 $\displaystyle 7706$

5239 $\displaystyle 5239$

20952 $\displaystyle 20952$

20956 $\displaystyle 20956$

Correct answer:

5239 $\displaystyle 5239$

Explanation:

First add all the numbers; then, divide by the amount of numbers in the set:

$\displaystyle 3257+1254+7485+8960=20956$

$20956\div 4=5239$ $\displaystyle 20956\div 4=5239$

Answer: The mean is 5239 $\displaystyle 5239$ .

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Example Question #93 : How To Find Mean

Find the mean of the following set:

$\displaystyle {6, 5, 8, 12, 6, 6, 5, 3, 12}$

Possible Answers:

$\displaystyle 9$

$\displaystyle 6$

$\displaystyle 7$

5.5 $\displaystyle 5.5$

$\displaystyle 12$

Correct answer:

$\displaystyle 7$

Explanation:

The mean is the sum of the numbers in the set divided by the number of values in the set:

$\frac{6+5+8+12+6+6+5+3+12}{9}=\frac{63}{9}=7$ $\displaystyle \frac{6+5+8+12+6+6+5+3+12}{9}=\frac{63}{9}=7$

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Example Question #115 : Data Analysis And Probability

Olivia is considering buying a new car. She is looking at three different cars. The price for the three cars is $\$8,789.00$ $\displaystyle \$8,789.00$ , $\$6,250.00$ $\displaystyle \$6,250.00$ and $\$9,342.00$ $\displaystyle \$9,342.00$ , respectively. What is the average price of a car Olivia is considering?

Possible Answers:

$\displaystyle 8, 127.00$

$\displaystyle 24,381.00$

$\displaystyle 12,190.00$

$\displaystyle 3,000.00$

Correct answer:

$\displaystyle 8, 127.00$

Explanation:

First add up the prices of each of the cars:

$\displaystyle 8,789.00+6,250.00+9,342.00=24,381$

Then divide that number by the total number of cars:

$24,381\div 3=8,127.00$ $\displaystyle 24,381\div 3=8,127.00$

Answer: The average price of a car Olivia is considering is $\$8,127.00$ $\displaystyle \$8,127.00$

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Example Question #95 : How To Find Mean

Find the mean of this set of numbers:

$\displaystyle 313, 529, 764, 910, 214$

Possible Answers:

657 $\displaystyle 657$

529 $\displaystyle 529$

546 $\displaystyle 546$

597 $\displaystyle 597$

Correct answer:

546 $\displaystyle 546$

Explanation:

First, add the numbers in the set:

$\displaystyle 313+529+764+910+ 214=2730$

Then divide by the amount of numbers in the set:

$2730\div 5=546$ $\displaystyle 2730\div 5=546$

Answer: The mean is 546 $\displaystyle 546$ .

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Example Question #115 : Data Analysis And Probability

Andy is grading the tests of $\displaystyle 12$ of his students and their results were as follows; $\displaystyle 95, 100, 100, 67, 89, 87, 71, 93, 88, 51, 100, 98$ . What is the average grade in the class?

Possible Answers:

82.3 $\displaystyle 82.3$

85.5 $\displaystyle 85.5$

$\displaystyle 90$

$\displaystyle 95$

86.6 $\displaystyle 86.6$

Correct answer:

86.6 $\displaystyle 86.6$

Explanation:

To find the average, you must first add up all of the test scores. The total is 1039 $\displaystyle 1039$ . Then you must divide that number by the number of test scores. Your final answer would be $\displaystyle 1039/12=86.6$ .

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SSAT Middle Level Math : How to find mean

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #91 : How To Find Mean

Example Question #465 : Data Analysis And Probability

Example Question #91 : Mean

Example Question #111 : Data Analysis And Probability

Example Question #91 : Mean

Example Question #92 : How To Find Mean

Example Question #93 : How To Find Mean

Example Question #115 : Data Analysis And Probability

Example Question #95 : How To Find Mean

Example Question #115 : Data Analysis And Probability

All SSAT Middle Level Math Resources

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