Statistics

• Arithmetic mean:
  Average = Sum / # of terms
  Sum = Average x (# of terms)
  To keep track of two average formulas in the same problem, you can set up an RTD style table.
• The average of an evenly spaced set is the middle number (or the arithmetic mean of two middle numbers). All you need to do to find the middle number is to find the arithmetic mean of the first and last terms.
• Weighted averages:
  Weighted average = (weight/sum of weights) x (data point) + (weight/sum of weights) x (data point) + ..
  or
  Weighted average = (weight)(data point) + (weight)(data point) / sum of weights
• Having just the ratios of the weights will allow you to find a weighted average. Simply write the ratio as a fraction, and use the numberator and the denominator as weights. If you know the weighted average you know the ratio of weights.
• If you know the two sub-group averages and you know the overall weighted average, then you can solve for the relative weightings of the two sub-groups. 
• If you are finding a weighted average of rates (whose units are fractions), then the "weights" correspond to the units appearing in the denominator of the rate.
• Median is the unique middle value of a set containg an odd number of values arranged in increasing (or decreasing) order, or the arithmetic mean of the two middle values of a set containing an even number of values arranged in increasing (or decreasing) order.
  You may be able to determine a specific value for the median of a set even if one or more unknowns are present.
• Solve problems involving both the arithmetic mean and the median by writing expressions for both.
• You may be required to construct and manipulate a completely abstract set, you can use alphabetical order to make it a little more concrete, or you can place the variables on an abstract number line in order to visualize their relationships, or you can create a column chart.
• Standard deviation indicates how far from the average (mean) the data points typically fall. The more spread out the numbers, the larger the SD.
  If you see a problem focusing on changes in the SD, ask yourself whether the changes move the data closer to the mean, farther from the mean, or neither. If the problem requires comparisons, ask yourself which set is more spread out from its mean.
  The term "variance" is the square of the SD.
• The mode of a set of numbers is the number that occurs most often.
• The range of a set of numbers is the difference between the largest number and the smallest number.