Freq - tabulation of observations

Average (Mean) - sum of observations divided by the number of observations.

Mode - most frequent observation

Median - point on a scale above which are exactly half the total observations and below which are the other half. 50th percentile. For example, with scores of 4, 5, 6, 8, and 25, the average is (4+5+6+8+25)/5 =48/5 = 9.6, but the median is 6 (the value in the middle). This tells us that there are some values that skew the distribution. Median is often used to report salaries.

Standard Deviation - The average difference between each observation and the mean. The probability that an observation is within 1 standard deviation from the mean is 68%. The probability that it is within 2 standard deviations is 95%. Standard deviation provides us with a measure to determine how close to the mean most of the observations are. A small standard deviation indicates that most of the observations are near the mean. A large standard deviation indicates that the observations are more widely dispersed. In almost all cases, you want to look at both the mean and the standard deviation. By looking at the mean and standard deviations of two samples, one can come to a statistical statement as to whether there is a statistical difference between the two sample. If the distributions overlap significantly, then they are said to show no significant statistical difference. Just knowing the averages does not give us that information.

Regression Analysis - provides us with a line through a series of points in which the difference between the points and the line are minimized. Used to compare two (or more) continuous variables (i.e.. height and weight). The general form of the line is y=mx+b where x and y are the variables (x is called the independent variable and y is called the depended variable) m is the slope of the line and b is where the line crosses the y axis. r is used to measure how well the line fits. r ranges from -1 (perfect negative correlation) to 1 (perfect positive correlation) 0 indicates no correlation r-square gives a measure which tells us the percent of the variation explained by the line. The higher the value, the better the correlation.

A WORD OF CAUTION: correlation does not mean that the two variables are related as to cause and effect. You can get a correlation between the stock market and your GPA and it would have no meaning. In summary, when looking single valued data, you want to know the average and the standard deviation. When looking at correlations between two (or more) variables, you want to know what the r or r-squared is. Without this additional measures it is hard to judge the data.