Begin by reordering the set in numerical order:

Then becomes

Since there is an odd number of values, the median is the middle value.

Quantity B: 

Now, to find the arithmetic mean, take the sum of values divided by the total number of values.

Quantity A: 

 is an unknown value, but it can be found given what we know about the mean of the set :

Now,  is out of order; arrange in numerically:

Since there are even number of values, the median is the mean of the two middle most values:

The arithmetic mean is the average of the sum of a set of numbers divided by the total number of numbers in the set. This is not to be confused with median or mode.

In Column A, the mean of 5.66 is obtained when the sum (17) is divided by the number of values in the set (3).

In Column B, the mean of 7 is obtained when 21 is divided by 3. Because 7 is greater than 5.66, Column B is greater. The answer is Column B.

Rate = distance/time.

Find the distance for each individual segment of the run (4 miles and 3.25miles). Then add total distance and divide by total time to get the average rate, while making sure the units are compatible (miles per hour not miles per minute), which means the total 45 minute run time needs to be converted to 0.75 of an hour; therefore (4miles + 3.25 miles/0.75 hour) is the final answer.

Note that:

The arithmetic mean of the 100 data points encompassing A and B = 

(total data of Sample Set A + total data of Sample Set B)/100

We have Mean of Sample Set A = 50, or:

(total of Sample Set A) / 25 = 50

And we have Mean of Sample Set B = 100, or:

We can calculate the arithmetic mean by adding up the numbers in a set, and dividing that total by the count of numbers in the set.

Thus, we know that (x + y + z) / 3 = 15. (Multiply both sides by 3.)

x + y + z = 45

We add w = 10 to that, and divide by the new count, 4.

55 / 4 = 13.75

Translate the question into a series of equations:

J + S = 130; J + S + A = 215; S + A = 137

Although there are several ways of approaching this, let us choose the path that is most direct.  Given that J, S, A are all involved in the second equation, we can isolate J if we eliminate S and A - which can be done by using the data we have in the third equation.  Since S + A = 137, we can rewrite J + S + A = 215 as:

J + 137 = 215.

Now, we only need to solve for J:

J = 215 - 137

J = 78 inches.

Begin by translating the current state of affairs into an equation.  We know that for four students, the average is ascertained by taking the sum of the scores (s) and dividing that by four:

s / 4 = 81; s = 324

Now, when we add the additional student, that person's score (x) will be added to the value for s.  The average of this new group will be divided among five students.  We must solve for the case in which the average is 83 points (thus giving us the case for the minimum score x necessary.)  This yields the following equation:

(324 + x) / 5 = 83

Solve for x:

324 + x = 415; x = 91

The minimum score necessary is 91 points.

To find the arithmetic mean of a series of numbers, add up all of the numbers and divide by the number of numbers in the series. Adding all the numbers gives us 40 and there are 8 numbers in the series. 40/8 = 5

Reorder the set: 55, 70, 81, 83, 88, 91

Since the set is even, we find the median by taking the average of the middle two values: (81 + 83)/2 = 82

The average of the first set = (55 + 70 + 81 + 83 + 88 + 91)/6 = 468/6 = 78

The new value to be added is 82 * 1.12 = 91.84

This means the new mean is 559.84/7 = 79.9771

The increase in mean value is 79.9771 – 78 = 1.9771

This is (1.9771/78) 100, or 2.535% larger than the original mean.