The median of a set of numbers is the value that falls in the middle of the set.
For example, if you have 5 test scores, and they are 88, 86, 57, 94, and 73, you must first list the scores in increasing or decreasing order: 57, 73, 86, 88, 94. The median is the middle number, or 86. If there is an even number of values in a set (6 test scores, for instance), simply take the average of the two middle numbers.
The mode of a set of numbers is the value that appears most often.
For example, if your test scores were 88, 57, 68, 85, 99, 93, 93, 84, and 81, the mode of the scores would be 93 because it appear more often than any other score.
If there is a tie for the most common value in a set, the set has more than one mode.
In direct variation, y = kx, where k is a constant. In direct variation, the variable y changes directly as x does. As x gets larger, y gets larger. For example, if a unit of Currency A is worth two units of Currency B, then A = 2B. If the number of units of B were to double, the number of units of A would double, and so on for halving, tripling, etc.
In inverse variation, xy = k, where x and y are variables and k is a constant. As x gets larger y gets smaller. A commonly used inverse relationship is rate x time = distance, where distance is constant. For example, imagine having to travel 24 miles. If you were to travel at 12 miles per hour, you'd need 2 hours. But if you were to travel at half your rate, you would have to double your time. This is just another way of saying that rate and time vary inversely.
To find the y-intercept, you can either put the equation into y = mx +b (slope-intercept form)-- in which case b, the constant term, is the y-intercept-- or you can just plug x = 0 into the equation and solve for y. For example, take 3x - y = 5.
Solving for y, if you put the equation in terms of y = mx + b form, you arrive at y = 3x - 5. The constant term, b, is -5 so the y-intercept is -5.
Using the other method, substitute 0 for x. 3(0) - y = 5 so y = -5. Again, the y-intercept is -5.
The midpoint of two points of a line segment is the average of the x-coordinates of the endpoints and the average of the y-coordinates of the endpoints. If the endpoints are (x^1, y^1) and (x^2, y^2), the midpoint is:
(x^1 + x^2) / 2, (y^1 + y^2) / 2
For example, the midpoint of (3,5) and (9,1) is:
(3 + 9) / 2, (1 + 5) / 2 = (12 / 2, 6 / 2) = (6,3)
To increase a number by a percent, add the percent to 100 percent, convert to a decimal, multiply.
For example, to increase 40 by 25 percent, add 25 percent to 100 percent, which equals 125%. Then, convert 125 percent to 1.25, and multiply by 40: 1.25 x 40= 50.
To decrease a number by a percent, subtract the percent from 100 percent, convert to a decimal, and multiply.
For example, to decrease 50 by 20 percent, subtract 20 percent from 100 percent, which equals 80%. Then, convert 80 percent to 0.80, and multipy by 50:0.80 x 50 = 40.
To convert a fraction to a decimal, divide the numerator by the denominator.
For example, to convert 5/8, divide 8 into 5, yielding .625.
To convert a decimal to a fraction, set the decimal over 1 and multiply the numerator and denominator by 10 raised to the number of digits to the right of the decimal point.
For example: to convert .625 to a fraction, you would multiply .625/1 by 10^3/10^3 or 1,000/1,000. Then, simplify: 625/1,000 = 5/8.