Ch. 4: Average & Standard Deviation Computing the average: –S–Sum of the values divided by the number of values. –E–Example: What is the average of the ages of the students in the first row? One measure of center is the average

Another measure of center is the median –The median is the 50 th percentile of the data. In other words, 50% of the data is greater than the median and 50% is less than the median. More simply stated, the median is the middle value when the data is put in order from least to greatest. –Example: What is the median age in the first two rows of students? First order the data. If it is an even number of values, take the average of the 2 middle numbers. If it is an odd number of values, pick the middle value in the ordered data.

Cross-sectional versus Longitudinal Studies Cross-sectional studies allows one to compare subjects to each other at one point in time. Longitudinal studies allows one to follow a subject over time and compare them to themselves over time. Examples: NHANES vs. Framingham Heart Studies

Comparing Averages and Medians The average is to the right of the median whenever the histogram has a long right tail. Example: US Census 2004 Median income: $45,996 Average income: $62,083

Standard Deviation How far data is from their average. Describes the spread of the data around the average. Roughly 68% of data are within 1 SD of the average. Roughly 95% of data are within 2 SDs of the average. These 2 statements are true most of the time but not always.

Calculating the SD 1.Find the average. 2.Find the deviation from the average for each data point. 3.Square the deviations. 4.Take the mean square of the square deviations (MS). 5.Take the square root of the MS (RMS). Example: 4, 4, 4, 4, 7