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Q
uantitative
R
easoning &
P
roblem
S
olving
294
© 2014 Pacific Crest
M
athematical Language
Terms and notation
a measure of central tendency
— a number that describes the central behavior of a set of data.
In particular it describes where data points cluster. There are three common measures of central
tendency, the mean, median and mode.
mean
— the arithmetic average of a set of numbers. It is determined by finding the sum of the elements
in a data set and then dividing by the number of elements in a data set. It is often denoted as:
x.
median
— the number in the middle of the data set. It is the 50
th
percentile. It is determined by listing
all of the data points in order from lowest to highest. If there are an odd number of data points, there
is a unique number in the middle and that is the median. If there is an even number of data points,
there are two numbers in the middle. Add those two numbers and then divide by two to determine
the median.
mode
— the data point that occurs most often. A set of data may have more than one mode.
nominal data
— data is listed in categories and there is no ordering scheme. Example: 0 = female,
1 = male.
ordinal data
— data is listed in categories but differences are meaningless. Example: List favorite
sports in order form 1 – 5. 1 = football, 2 = soccer, 3 = baseball, 4 = basketball, 5 = boxing.
interval data
— the differences between data values are meaningful but there is no “zero” so ratios are
meaningless. Example: 0 degrees Celsius does not mean lack of all heat, so data in degrees Celsius
is interval.
ratio data
— differences are relevant and there is a natural zero. Examples: Ages, degrees Kelvin,
odometer mileage.
symmetric
— the left half of the histogram is a mirror image of the right half of the histogram
skewed
— a data set is not symmetric and it extends much more to either the right or left side
outlier
— data points that are vastly different from the great majority of the other data points
I
nformation
What you need to know
R
eadings
R
esources
M
ethodology
C
onstructing
M
easures of
C
entral
T
endency
(CT)
Scenario:
Random Sample of Male Heights
Step
Explanation
1.
Describe the data
set
Is the set a random collection of data from a larger sample or is it a
convenience sample? What characteristic is being measured? What is the
relevant unit? Are there any specific conditions?
WATCH
IT WORK!
The set is a random collection of heights of males in the USA. The unit is in inches.
All data points are rounded to the nearest inch.