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PSAT Math : How to find arithmetic mean

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Example Questions

Example Question #31 : How To Find Arithmetic Mean

Daria plays darts often. She scores 25 points 1/5 of the time she plays. She also scores 50 points with probability 3/5, and 0 points with probability 1/5. What is the average number of points Daria scores when she plays darts?

Possible Answers:

Correct answer:

Explanation:

To find the average number of points, we need to multiply the points by their corresponding weights and sum them up.

Average = 1/5 * 25 + 3/5 * 50 + 1/5 * 0 = 35.

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Example Question #25 : How To Find Arithmetic Mean

Mrs. Hovsepian teaches 5 different math classes.

The first class contains 42 student. The second class has 38 students. The third class has 67 students. The fourth class has 25 students. The fifth class has 28 students.

What is the mean number of students per class?

Possible Answers:

Correct answer:

Explanation:

To get the mean we must add up all of the students and divide by the number of classes. When we add them all up there are 200 total students.

$\dpi{100} \small 200\div 5=40$

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Example Question #31 : How To Find Arithmetic Mean

Find the arithmetic mean of the following set of numbers:

$\dpi{100} \small 6,8,12,16,18$

Possible Answers:

$\dpi{100} \small 8$ $\displaystyle \dpi{100} \small 8$

$\dpi{100} \small 18$ $\displaystyle \dpi{100} \small 18$

$\dpi{100} \small 12$ $\displaystyle \dpi{100} \small 12$

$\dpi{100} \small 6$ $\displaystyle \dpi{100} \small 6$

$\dpi{100} \small 16$ $\displaystyle \dpi{100} \small 16$

Correct answer:

$\dpi{100} \small 12$ $\displaystyle \dpi{100} \small 12$

Explanation:

The mean is adding all the numbers then dividing by the number of items.

In this case we have, $\dpi{100} \small x-b,x-y,x,x+b,x+y$

where $\dpi{100} \small x=12, b= 6, y = 4$

When this happens, the average is $\dpi{100} \small x$ $\displaystyle \dpi{100} \small x$

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Example Question #31 : Statistics

$\small \textup{The average (arithmetic mean) of}\:x,\,y,\,\textup{and}\,z\,\textup{is 8.}$

$\small \textup{If}\,y=5x\,\textup{and}\,z=6,\,\textup{what is the value of}\,x?$

Possible Answers:

$\small 3$ $\displaystyle \small 3$

$\small 8$ $\displaystyle \small 8$

$\small 6$ $\displaystyle \small 6$

$\small 5$ $\displaystyle \small 5$

$\small 15$ $\displaystyle \small 15$

Correct answer:

$\small 3$ $\displaystyle \small 3$

Explanation:

Arithmetic mean: $\small \left ( x+y+z\right )\div3=8$ $\displaystyle \small \left ( x+y+z\right )\div3=8$ given: $\small z=6\;\;y=5x$ $\displaystyle \small z=6\;\;y=5x$

Solve: $\small \left ( x+5x+6\right )\div3=8$ $\displaystyle \small \left ( x+5x+6\right )\div3=8$

$\small 6x+6=24$ $\displaystyle \small 6x+6=24$

$\small 6x=18$ $\displaystyle \small 6x=18$

$\small x=3$ $\displaystyle \small x=3$

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Example Question #32 : Data Analysis

A class consists of 10 students. The teacher wrote the test and expects the class to have an average score of at least 80. The average score of 9 people was calculated and it was 78. What score does the last person have to get in order to reach the teacher's standard?

Possible Answers:

$100$ $\displaystyle 100$

$88$ $\displaystyle 88$

$98$ $\displaystyle 98$

$94$ $\displaystyle 94$

$82$ $\displaystyle 82$

Correct answer:

$98$ $\displaystyle 98$

Explanation:

The total score of those 9 students is $9\cdot 78=702$ $\displaystyle 9\cdot 78=702$ .

The standard score for the entire class was $10\cdot 80=800$ $\displaystyle 10\cdot 80=800$ .

Therefore, the last person needs a score of $800-702=98$ $\displaystyle 800-702=98$ .

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Example Question #31 : How To Find Arithmetic Mean

What is the average (mean) of

$2x+7, 3x-10, and\ -14x+12$ $\displaystyle 2x+7, 3x-10, and\ -14x+12$

Possible Answers:

4x+7 $\displaystyle 4x+7$

-3(x-1) $\displaystyle -3(x-1)$

-3(x+1) $\displaystyle -3(x+1)$

3(x+1) $\displaystyle 3(x+1)$

3(x-1) $\displaystyle 3(x-1)$

Correct answer:

-3(x-1) $\displaystyle -3(x-1)$

Explanation:

By adding all of the expressions we get -9x+9 $\displaystyle -9x+9$

which averages to -3x+3 $\displaystyle -3x+3$ ,

which will simplify to -3(x-1) $\displaystyle -3(x-1)$ .

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Example Question #31 : How To Find Arithmetic Mean

The mean of a series of 6 numbers (11, 12, 14, 17, 18, x) is 15. Solve for x.

Possible Answers:

Correct answer:

Explanation:

If the mean of 6 numbers is 15, that implies that the sum of the numbers is equal to 90 (6 x 15).

Therefore, $\small 90=(11+12+14+17+18+x)$ $\displaystyle \small 90=(11+12+14+17+18+x)$ or $\small 90=(72+x)$ $\displaystyle \small 90=(72+x)$ $\small 90-72=x=18$ $\displaystyle \small 90-72=x=18$

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Example Question #32 : How To Find Arithmetic Mean

A police officer walked into a room full of suspects and turn out their pockets. The chart below shows the number of coins each man had.

Screen_shot_2013-09-04_at_10.20.59_am

The police claim the man with the amount of money closest to the arithmetic mean of the group is guilty. Who is it?

Possible Answers:

Suspect 3

Suspect 1

Suspect 4

Suspect 6

Suspect 2

Correct answer:

Suspect 2

Explanation:

Screen_shot_2013-09-04_at_10.26.20_am

Summing total money and dividing by the number of suspects gives us an average of approximately $2.73. By comparing it to the amounts held by the suspects, we can see that Suspect #2 is guilty.

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Example Question #31 : How To Find Arithmetic Mean

The average temperature for 6 days in July is $87^\circ F$ $\displaystyle 87^\circ F$ . If on the seventh day, the temperature is $54^\circ F$ $\displaystyle 54^\circ F$ , what is the average temperature over those seven days?

Possible Answers:

$76.0^\circ F$ $\displaystyle 76.0^\circ F$

None of the available answers.

$70.5^\circ F$ $\displaystyle 70.5^\circ F$

$82.3^\circ F$ $\displaystyle 82.3^\circ F$

There is not enough information to answer this question.

Correct answer:

$82.3^\circ F$ $\displaystyle 82.3^\circ F$

Explanation:

In order to calculate mean, we can act as though the temperature was exactly $87^\circ F$ $\displaystyle 87^\circ F$ for the first six days and $54^\circ F$ $\displaystyle 54^\circ F$ on the seventh day. The mean can be expressed:

$\frac{(6\times 87)+54}{7}=\frac{522+54}{7}=\frac{576}{7}\approx 82.3^\circ F$ $\displaystyle \frac{(6\times 87)+54}{7}=\frac{522+54}{7}=\frac{576}{7}\approx 82.3^\circ F$

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Example Question #34 : How To Find Arithmetic Mean

If the average of $b + 2$ $\displaystyle b + 2$ is equal to the average of $b + 4 + 6$ $\displaystyle b + 4 + 6$ . What is the value of $b$ $\displaystyle b$ ?

Possible Answers:

Correct answer:

Explanation:

$\frac{b+2}{2}=\frac{b+4+6}{3}$ $\displaystyle \frac{b+2}{2}=\frac{b+4+6}{3}$

$3b+6=2b+8+12$ $\displaystyle 3b+6=2b+8+12$

$b=14$ $\displaystyle b=14$

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PSAT Math : How to find arithmetic mean

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #31 : How To Find Arithmetic Mean

Example Question #25 : How To Find Arithmetic Mean

Example Question #31 : How To Find Arithmetic Mean

Example Question #31 : Statistics

Example Question #32 : Data Analysis

Example Question #31 : How To Find Arithmetic Mean

Example Question #31 : How To Find Arithmetic Mean

Example Question #32 : How To Find Arithmetic Mean

Example Question #31 : How To Find Arithmetic Mean

Example Question #34 : How To Find Arithmetic Mean

All PSAT Math Resources

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