Chapter 4 – Measurements of Location and Position Math 22 Introductory Statistics

Means Population Mean (  ) - Numerical value that locates the balance point (also called the center of mass) of the population distribution. Sample Mean - Generated from a sample of observation x 1,x 2,x 3,...,x n

Median Population Median Sample Median Median Vs. Mean Mean can be moved a great deal with extreme scores, the median cannot. Mode

Quartiles and Five Number Summary Quartiles (First, Second, Third) Five Number Summary

Looking at a Distributions Box Plot Multimodial Distributions Box Plot vs. Histograms

Percentiles Percentile – the location where a specified percentage of the data falls below that point.

Procedure for Finding Percentiles Sort the data from smallest to largest. Find the location by multiplying the sample size n, by the proportion represented on the percentile. If the location calculated is a non-integer value, round up to the next integer value. Identify the data value in that position as the desired percentile.

Procedure for Finding Percentiles If the location calculated is an integer value, average the data value in that position and the next position. The average of the two values will be identified as the desired percentile.