INFO HW
INFO 1010
SINGLE VARIABLE
CENTRAL TENDENCY MEASURES
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1
Measures of Location
If the measures are computed
for data from a sample, they
are called sample statistics.
If the measures are computed for
data from a population, they are
called population parameters.
A sample statistic is referred to as
the point estimator of the
corresponding population parameter.
Mean
Median
Mode
Percentiles
Quartiles
Weighted Mean
Geometric Mean
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Sample Mean
Number of
observations
in the sample
Sum of the values
of the n observations
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Population Mean m
Number of
observations in
the population
Sum of the values
of the N observations
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Weighted Mean
Denominator:
sum of the
weights
Numerator:
sum of the weighted
data values
If data is from
a population,
m replaces .
where:
xi = value of observation i
wi = weight for observation i
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Geometric Mean
= [(x1)(x2)…(xn)]1/n
Excel’s geometric mean function is:
=GEOMEAN(data cell range)
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Excel Formula Worksheet
Using Excel to Compute the Mean, Median, and Mode
A
B
C
D
E
1
Apart-
ment
Monthly
Rent ($)
2
1
545
Mean
=AVERAGE(B2:B71)
3
2
715
Median
=MEDIAN(B2:B71)
4
3
530
Mode
=MODE.SNGL(B2:B71)
5
4
690
6
5
535
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Percentiles
A percentile provides information about how the data are spread over the interval from the smallest value to the largest value.
Admission test scores for colleges and universities are frequently reported in terms of percentiles.
The pth percentile of a data set is a value such that at least p percent of the items take on this value or less and at least (100 - p) percent of the items take on this value or more.
PERCENTILE.EXC(data range, p/100)
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Quartiles
Quartiles are specific percentiles.
First Quartile = 25th Percentile
Second Quartile = 50th Percentile = Median
Third Quartile = 75th Percentile
QUARTILE.EXC (data range, quartile number)
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