**Unformatted text preview: **What you will learn in Chapter 2
– Measures of central tendency
– Computing the mean for a set of scores
– Computing the mode and median for a set of
scores
– Selecting a measure of central tendency
Salkind, Statistics for People Who (Think
They) Hate Statistics 5th Edition, SAGE Inc.
© 2014 Measures of Central Tendency
• The AVERAGE is a single score that best
represents a set of scores
• Another name for AVERAGES is Measures
of Central Tendency
• Examples include the mean, median, and
mode
Salkind, Statistics for People Who (Think
They) Hate Statistics 5th Edition, SAGE Inc.
© 2014 Computing the Mean
• • (X Bar) is the mean value of the group of scores
• (sigma) tells you to add together whatever follows it
• X is each individual score in the group
• The n is the sample size Salkind, Statistics for People Who (Think
They) Hate Statistics 5th Edition, SAGE Inc.
© 2014 Steps to Computing the Mean
1. List the entire set of values in one or more
columns. These are all the Xs.
2. Compute the sum or total of all the values.
3. Divide the total or sum by the number of
values.
Salkind, Statistics for People Who (Think
They) Hate Statistics 5th Edition, SAGE Inc.
© 2014 Things to remember…
• N = population n = sample • Sample mean is the measure of central tendency that best
represents the population mean
• It is also called the arithmetic mean
– Mean is the centermost point where all the values on one side of the
mean are equal in weight to all the values on the other side of the
mean • Mean is VERY sensitive to extreme scores that can “skew”
or distort findings
Salkind, Statistics for People Who (Think
They) Hate Statistics 5th Edition, SAGE Inc.
© 2014 Weighted Mean
• Step 1: List all values for which the mean is being
calculated (list them only once)
• Step 2: List the frequency (number of times) that value
appears
• Step 3: Multiply the value by the frequency
• Step 4: Sum all Value x Frequency
• Step 5: Divide by the total Frequency (total n size)
Salkind, Statistics for People Who (Think
They) Hate Statistics 5th Edition, SAGE Inc.
© 2014 Median
• point/score at which 50% of remaining
scores fall below it and 50% fall above it Salkind, Statistics for People Who (Think
They) Hate Statistics 5th Edition, SAGE Inc.
© 2014 Steps to Finding the Median
1) List the values, in order, either from
highest to lowest or lowest to highest.
2) Find the middle-most score. That’s the
median. Salkind, Statistics for People Who (Think
They) Hate Statistics 5th Edition, SAGE Inc.
© 2014 BUT…
• What if there are two middle scores?
• What if the two middle scores are the
same? Salkind, Statistics for People Who (Think
They) Hate Statistics 5th Edition, SAGE Inc.
© 2014 A little about Percentiles…
• Percentile ranks are used to define the
percent of cases equal to and below a certain
point on a distribution
• 75th %tile – means that the score received is
at or above 75 % of all other scores in the
distribution
• Median is always at the 50th percentile
Salkind, Statistics for People Who (Think
They) Hate Statistics 5th Edition, SAGE Inc.
© 2014 Things to Remember
• The mean is the middle point of a set of values,
while the median is the middle point of a set of
cases
• Because the median cares about the number of
cases, extreme scores (i.e., outliers) do not
impact it
• Sometimes people use Mdn or Med to stand for
median
Salkind, Statistics for People Who (Think
They) Hate Statistics 5th Edition, SAGE Inc.
© 2014 Computing the Mode
• Mode = most frequently occurring score
• This is the least precise measure of central
tendency
• When two values occur the same number
of times -- Bimodal distribution Salkind, Statistics for People Who (Think
They) Hate Statistics 5th Edition, SAGE Inc.
© 2014 Steps to Finding Mode
• List all values in the distribution
• Tally the number of times each value occurs
• The value occurring the most is the mode Salkind, Statistics for People Who (Think
They) Hate Statistics 5th Edition, SAGE Inc.
© 2014 Example of Finding Mode
Party Affiliation Number or Frequency Democrats 90 Republicans 70 Independents 140 Salkind, Statistics for People Who (Think
They) Hate Statistics 5th Edition, SAGE Inc.
© 2014 When to Use What…
• Use Mode: when the data are qualitative,
categorical, or nominal (e.g., eye color,
political party)and values can only fit into
one category (i.e., mutually-exclusive)
• Use Median when you have extreme scores
• Use Mean when the data does not include
extreme scores (i.e., outliers) and are not
qualitative, categorical, or nominal
Salkind, Statistics for People Who (Think
They) Hate Statistics 5th Edition, SAGE Inc.
© 2014 Skewed Distribution
• A distribution of scores has a high
number of scores clustered at one end
of the distribution with relatively few
scores spread out toward the other
end of the distribution, forming a tail. • Similarities between a skewed and
normal distribution:
• • The procedures used to calculate a
mean, median, and mode are the same Differences between a skewed and
normal distribution:
• The position of the three measures of
central tendency in the distribution Example: The Mean, Median, and Mode of a
Distribution
The following distribution of test scores are given: 86 90 96 96 100 105 115 121 Mean = 86+90+96+96+100+105+115+121 = 101.13
8
Calculating the mean: Add up all the scores, then divide by the number of scores.
In this case, there are 8 IQ scores. Median = 96+100 = 98
2
Calculating the median: Because there is an even amount of scores, sum the two
scores that are found in the middle of the distribution when it is put into
numerical order, then divide by two. Mode = 96
Calculating the mode: 96 is the most frequent number that occurs in the
distribution Using SPSS Salkind, Statistics for People Who (Think
They) Hate Statistics 5th Edition, SAGE Inc.
© 2014 ...

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