Construction Engineering 221
Probability and Statistics
Location Measurement
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
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
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
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)
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)
Location Measures
• Examples:
– Σi, i=1,n=10 means 1+2+3+4+5+6+7+8+9+10
– Σ ƒ I=1, n=10 means 1 + 2 + 3 …+ 10
– Mean (Xbar) is Σ xi, i=1, n=n
n
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.