Definitions of Terms

One Variable Terms

mean

The mean is one measure of central tendency. It is the physical balancing point. Picture the data as blocks on a seesaw. It is computed by adding up the data and dividing by how many numbers there are.
Other measures of central tendency are the median and the mode. The mode is the most frequently occurring value in the data. If the data is graphed on a histogram, the mode will be the highest point.
The median is the value in the list for which 50% of the list is less than that value and 50% is more than that value.

standard deviation for populations

The standard deviation is a measure a variation - it tells you how spread-out the data is. A small standard deviation implies a compact list. A large standard deviation implies a more spread-out list. The population is the group of whatever it is you want to measure. (For instance, if you are interested in the salaries of people in Illinois, then people in Illinois is your population.)

standard deviation for samples

The standard deviation is a measure a variation - it tells you how spread-out the data is. A small standard deviation implies a compact list. A large standard deviation implies a more spread-out list. A sample is a small group taken from a large population. Samples are used because populations are usually so large that calculations become unfeasible. (For instance, it would be impossible to check the salaries of everybody in Illinois.)

Two Variable Terms

correlation coefficient (r)

The correlation of two groups of data is a measure of the linear relationship between them - that is, how close a graph of the data is to a straight line. The correlation is a number between -1 and 1. A correlation close to 1 implies almost a straight line with positive slope. A correlation close to -1 implies almost a straight line with negative slope. A correlation close to 0 implies no linear relationship.

regression line - slope and intercept

Assuming that the relationship is linear, the regression line is the most plausible candidate for what the line is. The slope indicates how steep the line is. More precisely, the slope tells you the change in the y-variable that corresponds to a 1-unit change in the x-variable. The y-intercept indicates where the lines crosses (or intercepts) the y-axis. This is the y-value that corresponds to an x-value of 0.

Combinatorics

combinations

The expression _nC_r tells you the number of ways of choosing r distinct objects from a set of n objects. ( is another common notation.) An example is ₄₉C₆, the number of ways of choosing six Lotto numbers from a set of 49 possible numbers. Note that the order of numbers is not important here - 2, 4, 6, 8, 10, 12 is the same choice as 8, 12, 2, 6, 4, 10.
The formula is where n! is the product of the integers from 1 to n.
(E.g., 6! = 1*2*3*4*5*6 = 720.)

permutations

The expression _nP_r tells you the number of ways of arranging r distinct objects from a set of n objects. An example is ₁₀P₄, the number of different four-digit PIN numbers that can be made, assuming the four digits are all different. Note that order is important here. 1234 is not the same PIN number as 3142.
The formula is where n! is the product of the integers from 1 to n.
(E.g., 6! = 1*2*3*4*5*6 = 720.)

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One Variable Terms
	mean
		The mean is one measure of central tendency. It is the physical balancing point. Picture the data as blocks on a seesaw. It is computed by adding up the data and dividing by how many numbers there are. Other measures of central tendency are the median and the mode. The mode is the most frequently occurring value in the data. If the data is graphed on a histogram, the mode will be the highest point. The median is the value in the list for which 50% of the list is less than that value and 50% is more than that value.
	standard deviation for populations
		The standard deviation is a measure a variation - it tells you how spread-out the data is. A small standard deviation implies a compact list. A large standard deviation implies a more spread-out list. The population is the group of whatever it is you want to measure. (For instance, if you are interested in the salaries of people in Illinois, then people in Illinois is your population.)
	standard deviation for samples
		The standard deviation is a measure a variation - it tells you how spread-out the data is. A small standard deviation implies a compact list. A large standard deviation implies a more spread-out list. A sample is a small group taken from a large population. Samples are used because populations are usually so large that calculations become unfeasible. (For instance, it would be impossible to check the salaries of everybody in Illinois.)

Two Variable Terms
	correlation coefficient (r)
		The correlation of two groups of data is a measure of the linear relationship between them - that is, how close a graph of the data is to a straight line. The correlation is a number between -1 and 1. A correlation close to 1 implies almost a straight line with positive slope. A correlation close to -1 implies almost a straight line with negative slope. A correlation close to 0 implies no linear relationship.
	regression line - slope and intercept
		Assuming that the relationship is linear, the regression line is the most plausible candidate for what the line is. The slope indicates how steep the line is. More precisely, the slope tells you the change in the y-variable that corresponds to a 1-unit change in the x-variable. The y-intercept indicates where the lines crosses (or intercepts) the y-axis. This is the y-value that corresponds to an x-value of 0.

Combinatorics
	combinations
		The expression _nC_r tells you the number of ways of choosing r distinct objects from a set of n objects. ( is another common notation.) An example is ₄₉C₆, the number of ways of choosing six Lotto numbers from a set of 49 possible numbers. Note that the order of numbers is not important here - 2, 4, 6, 8, 10, 12 is the same choice as 8, 12, 2, 6, 4, 10. The formula is where n! is the product of the integers from 1 to n. (E.g., 6! = 12345*6 = 720.)
	permutations
		The expression _nP_r tells you the number of ways of arranging r distinct objects from a set of n objects. An example is ₁₀P₄, the number of different four-digit PIN numbers that can be made, assuming the four digits are all different. Note that order is important here. 1234 is not the same PIN number as 3142. The formula is where n! is the product of the integers from 1 to n. (E.g., 6! = 12345*6 = 720.)