GMAT Quantitative - Calculating arithmetic mean

The average of 10, 25, and 70 is 10 more than the average of 15, 30, and x. What is the missing number?

$30$

$25$

$15$

$20$

$35$

Explanation

The average of 10, 25, and 70 is 35: $\frac{10+25+70}{3}=35$

So the average of 15, 30, and the unknown number is 25 or, 10 less than the average of 10, 25, and 70 (= 35)

so $\frac{15+30+x}{3}=25$

$15+30+x=75$

$45+x=75$

$x=30$

What is the mean of the following data set in terms of and ?

$\left {a -x, a, a + x, a + 2x, 2a-x, 2a, 2a+x, 2a+2x \right }$

$\frac{3}{2} a +\frac{1}{2} x$

$\frac{3}{2} a -\frac{1}{2} x$

$\frac{3}{2} a$

Explanation

Add the expressions and divide by the number of terms, 8.

The sum of the expressions is:

$\left (a -x \right ) + a + \left ( a + x \right ) +\left ( a +2x \right ) + \left ( 2a-x \right ) + 2a + \left ( 2a+x \right ) +\left ( 2a+2x \right )$

Divide this by 8:

$\left ( 12a + 4x \right )\div 8 =\frac{3}{2} a +\frac{1}{2} x$

Find such that the arithmetic mean of is equal to the arithmetic mean of

Explanation

The formula for the arithmetic mean is:

Mean= $\frac{x_{1}+x_{2}+...+x_{n}}{n}$

We can then write:

$\frac{n+13+27+35}{4}=\frac{20+16+41+23}{4}$

The average of the following 6 digits is 75. What is a possible value of ?

80, 78, 78, 70, 71,

Explanation

Therefore, the sum of all 6 digits must equal 450.

Subtract 377 from both sides.

When assigning a score for the term, a professor takes the mean of all of a student's test scores except for his or her lowest score.

On the first five exams, Donna has achieved the following scores: 76, 84, 80, 65, 91. There is one more exam in the course. Assuming that 100 is the maximum possible score, what is the range of possible final averages she can achieve (nearest tenth, if applicable)?

Minimum 79.2; maximum 86.2

Minimum 66; maximum 71.8

Minimum 66; maximum 99.2

Minimum 79.2; maximum 99.2

Minimum 80, maximum 84

Explanation

The worst-case scenario is that she will score 65 or less, in which case her score will be the mean of the scores she has already achieved.

$\frac{76+ 84+80+65+ 91}{5} = 79.2$

The best-case scenario is that she will score 100, in which case the 65 will be dropped and her score will be the mean of the other five scores.

$\frac{76+ 84+80+ 91+100}{5} = 86.2$

If and , then give the mean of , , , , and .

Insufficient information is given to answer this question.

Explanation

The mean of , , , , and is $\frac{1}{5} \left (a + b + c + d + e \right )$

If you add both sides of each equation:

$\underline{5a + 4b + 3c + 2d + e = 5,300}$

$6\left (a + b + c + d + e \right )= 8,700$

Equivalently,

$6\left (a + b + c + d + e \right ) \div 6= 8,700 \div 6$

$\frac{1}{5} \left (a + b + c + d + e \right )= \frac{1}{5} \cdot 1,450 = 290$ ,

making 290 the mean.

The average high temperature for the week is 85. The first six days of the week have high temperatures of 89, 76, 92, 90, 80, and 84, respectively. What is the high temperature on the seventh day of the week?

Explanation

$average = \frac{sum}{days}$

$85=\frac{89+76+92+90+80+84+x}{7}=\frac{511+x}{7}$

What is the mean of this data set?

$\left { 1, 0.1, 0.01, 0.001, 0.0001, 0.00001 \right }$

Explanation

Add the numbers and divide by 6:

$\left (1 + 0.1 + 0.01 + 0.001+ 0.0001 + 0.00001 \right )\div 6$

$= 1.11111\div 6 = 0.185185$

A bakery sold a daily average of 25 croissants last week. The table above shows the number of croissants sold each day except Sunday. Find the number of croissants sold on Sunday.

Explanation

Let be the number of croissants sold on Sunday. The daily average of croissants sold in the past week is:

$\frac{29+15+12+10+34+38+x}{7}=25$

Solve for :

The number of croissants sold on Sunday is .

Salaries for employees at ABC Company: 1 employee makes $25,000 per year, 4 employees make $40,000 per year, 2 employees make $50,000 per year and 5 employees make $75,000 per year.

What is the average (arithmetic mean) salary for the employees at ABC Company?

$\dpi{100} \small $ 55,000$

$\dpi{100} \small $ 46,250$

$\dpi{100} \small $ 48,640$

$\dpi{100} \small $ 53,500$

$\dpi{100} \small $ 58,000$

Explanation

The average is found by calculating the total payroll and then dividing by the total number of employees. $\frac{(1\cdot 25,000)+(4\cdot 40,000)+(2\cdot 50,000)+(5\cdot 75,000)}{1+4+2+5}$

$\frac{25,000+160,000+100,000+375,000}{12} = \frac{660,000}{12}= $55,000$

Calculating arithmetic mean

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