Download Intro to Stats - Heather Lench, Ph.D.

Measures of
Central Tendency
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Parentheses
Exponents
Multiplication or division
Addition or subtraction
*remember that signs form the skeleton of
the formula
◦ X + Y / 2 (divide y by 2 and add to x)
◦ X + Y (add X and Y, then divide by 2)
2
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Number that best represents a group of scores
Represents the “typical” individual
Describes a large amount of data with a single
number
No single measure is best
Mean
Median
Mode
Each gives different information about a group of
scores
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A measure of where most values tend to
fall in a dataset
What we often refer to as an “average”
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Sum the values in a group & divide by number
of values
*Every score is represented
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X = ΣX/n
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X= mean value of a group of scores
Σ = summation sign
X = each score in the set
n = sample size in set
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Data: 41, 38, 56, 19, 31, 14, 52, 35, 34,
10, 38, 39, 20
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Most reliable and most often used
Isn’t necessarily an actual score
Strongly influenced by outliers
Sum of the deviations equals zero
Score (X)
X-X
1
-2.56
5
1.44
2
-1.56
1
-2.56
2
-1.56
12
8.44
3
-.56
2
-1.56
4
0.44
SUM
-.04
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Multiply the value by the frequency of
occurrence for each value, sum all the values,
then divide by total frequency
First
Sample
Second
Sample
n = 12
n=8
M=6
M=7
ΣX = 72
ΣX = 56
Combined
Sample
n = 20
ΣX = 128
M = 6.4
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Midpoint in a set of scores
50% below and 50% above the median value
No formula to compute
List values in order, from lowest to highest &
find the middle score
If there are 2 middle scores, find the mean of
these 2 scores
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Data: 41, 38, 56, 19, 31, 14, 52, 35, 34,
10, 38, 39, 20
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The median is not sensitive to extreme scores
and can be the most accurate centermost
value (i.e., average)
Means can skew due to extreme scores
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Value that occurs most frequently
No formula to compute
List all values once, tally the number of times
each occurs, find the value that occurs most
frequently
Can have bimodal or multimodal sets
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Only way to capture an average for nominal
data
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Data: 41, 38, 56, 19, 31, 14, 52, 35, 34,
10, 38, 39, 20
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Nominal data can only be described with the
mode
The mean is usually the most precise with
interval/ratio data
Median is best in the presence of extreme
values or if some values are imprecise
*You might report more than one
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1. When you have extreme scores or skew
2. When you have undetermined values
3. When you have an ordinal scale
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1. When you have a nominal scale (and
sometimes ordinal)
2. When you have discrete variables
3. When you are interested in describing the
shape of a distribution
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When asked to write as you would for a journal
◦ Write the statistic of central tendency to 2 decimal
places
◦ Clearly state what you are reporting
◦ Include the units of measurement
 The mean time to run a mile was 2.7 minutes
 The median home price in Texas is $80,000.
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When asked to interpret a finding “for someone
unfamiliar with statistics”
◦ Describe the meaning of the statistic rather than using
jargon
◦ Include the units of measurement
 The average runner completed a mile in about 2.7 minutes
 The middlemost home price in Texas is $80,000