1. Construction Engineering 221
Probability and Statistics
Location Measurement

2. Location Measures
Just like geographical location, statistical location uses a point of reference (mean, median, mode) and a distance (dispersion) from the reference point, or variance
In normal distributions, the location measures reference the center of the distribution, or the most common measurement or observation

3. Location Measures
Midrange, mode, median, and mean are the standard measures of location
Mode and midrange are seldom used, although mode can be helpful in some analyses (lots of zeroes, for example) to get an estimation of bias or validity
Midrange is the halfway point
Largest measure-smallest measure/2

4. Location Measures
Mode observation or measure occurring most frequently- no repeating measures, the sample has no mode, some observations repeated the same number of times, the sample is multimodal
Median- middle observation; the score or measure which has the same number of scores below as above

5. Location Measures Mean- Xbar + x1 + x2 + x3…xi/n
n = number of observations or sample size
Mean is good for comparing different samples (drug testing) and for powerful statistical tests
Median is better measure of center when there are “outliers” or when the data is presented in classifications (can’t use mean)

6. Location Measures
Median is the n/2 observation of rank ordered data. Can also be a classification (median grade was a “C”)
Summation notation uses Sigma (Σ), with index of summation i and limit of summation n over a function or expression (ƒ)

7. Location Measures Examples: Σi, i=1,n=10 means 1+2+3+4+5+6+7+8+9+10
Mean (Xbar) is Σ xi, i=1, n=n n

8. Location Measures
In classifications, can take the mark times the frequency, and sum the multiples
When added to measures of variance (dispersion), measures of location can be used to numerically describe a distribution of data and also to test some assumptions about the data, estimations of chance and probability, etc.