Wednesday, September 26 Appreciating the beautiful world of data…

…using your eyeballs and your brain

Types of data Nominal Ordinal Interval/Ratio Think of these in terms of information value!

Current NL West Baseball Standings

Looking at Distributions Frequency distributions Stem-and-Leaf Display

Central tendency

The mode is the score with the highest frequency of occurrences. It is the easiest score to spot in a distribution. It is the only way to express the central tendency of a nominal level variable.

The median. The median is the middle-ranked score (50th percentile). If there is an even number of scores, it is the arithmetic average of the two middle scores. The median is unchanged by outliers. Even if Bill Gates were deleted from the U.S. economy, the median asset of U.S. citizens would remain (more or less) the same.

 The Mean The mean is the arithmetic average of the scores. Xi _ _________ i X = N

 The Mean The mean is the arithmetic average of the scores. The mean is the center of gravity of a distribution. Deleting Bill Gates’ assets would change the national mean income.  Xi _ _________ i X = N

The mean of a group of scores is that point on the number line such that the sum of the squared distances of all scores to that point is smaller than the sum of the squared distances to any other point.

The Mean The sum of squared deviations from the Mean is at the lowest value. _ ( ) 2  Xi - X is lowest

The Mean The sum of squared deviations from the Mean is at the lowest value. _ ( ) 2  Xi - X is lowest _ X

The Mean The mean is the arithmetic average of the scores. The mean is the center of gravity of a distribution. Deleting Bill Gates’ assets would change the national mean! The sum of squared deviations from the Mean is at the lowest value. The mean is not a good measure of central tendency if there are outliers.

Variability

For the eyeball: Range, Interquartile Range Range: Highest minus lowest score. Interquartile Range: 75th percentile score minus 25th percentile score.

SS Variance of a population, 2 (sigma squared). It is the sum of squares divided (SS) by N SS 2 = N

SS Variance of a population, 2 (sigma squared). It is the sum of squares divided (SS) by N  (X –  ) 2 SS 2 = N

The Standard Deviation of a population,  It is the square root of the variance. SS  = N This enables the variability to be expressed in the same unit of measurement as the individual scores and the mean.