One Variable Terms |
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mean |
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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. |
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standard deviation for
populations |
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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.) |
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standard deviation for
samples |
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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.) |
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Two Variable Terms |
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correlation coefficient
(r) |
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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 |
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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. |
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Combinatorics |
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combinations |
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The expression _{n}C_{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 _{49}C_{6}, 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. |
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permutations |
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The expression _{n}P_{r} tells you the
number of ways of arranging r distinct objects from a set of n objects. An
example is _{10}P_{4}, 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. |