Download MEASURE OF CENTRAL TENDENCY AND DISPERSION

MEASURE OF CENTRAL TENDENCY AND DISPERSION
OBJETIVES
• By the end of this session students will be able to:
– Define biostatics.
– Enlist uses of biostatics.
– Appreciate role of biostatician.
– Enlist and calculate measures of central tendency and
dispersion.
INTRODUCTION
• ONE WAY TO UNDERSTANDING BIOSTATISTICS IS TO
CONSIDER TWO BASIC QUESTIONS:
– WHAT DOES THE TERM STATISTICS MEAN?
– WHAT DO STATISTICIANS DO?
• ONCE WE HAVE THE ANSWERS TO THESE QUESTIONS,
WE CAN DELVE INTO HOW STATISTICS ARE USED.
“STATISTICS”
• The word statistics frequently used to refer to recorded data
such as the number of traffic accidents, the number of patients
visiting a clinic or etc.
• Statistics is also used to denote characteristics calculated for a
set of data –for example, mean, standard deviation, and
correlation coefficient.
• In short, statistics is a body of techniques and procedures
dealing with the collection, organization, analysis, interpretation.
And presentation of information that can be stated numerically.
WHAT DO STATISTICIANS DO?
• A statistician is usually a member of a group that works on
challenging scientific tasks. Frequently engaged in projects that
explore the frontiers of human knowledge, the statistician is
primarily concerned with developing and applying methods that
can be used in collecting and analyzing data.
• One may select a well-established technique or develop a new
one that may provide a unique approach to a particular study
,thus leading to valid conclusions.
STASTICIAN’ TASKS
• TO GUIDE THE DESIGN OF AN EXPERIMENTS OR
SURVEYS
• TO ANALYZE DATA
• TO PRESENT AND INTERPRET RESULTS
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Measures of Central Tendency and Dispersion
Why Describe Central Tendency?
Data often cluster around a central value that lies between the
two extremes. This single number can describe the value of
scores in the entire data set
There are three measures of central tendency.
1) Mean
2) Median
3) Mode
THE MODE
The mode is the most frequently occurring number in a set of
data
• E.g., find the mode of the following numbers…
• 15, 20, 21, 23, 23, 23, 25, 27, 30
Also, if there are two modes, the data set is bimodal
If there are more than two modes, the data set is said to be
multimodal
The Median
The middle score when all scores in the data set are arranged
in order.
Half the scores lie above and half lie below the median.
E.g., find the median of the following numbers…
• When there is an even number of scores, you must take the
average of the middle two scores.
THE MEAN
• This is the sum of all the scores data set divided by the number
of scores in the set.
• The mean can also be calculated using a frequency distribution.
• The following scores were obtained on a stats exam marked out
of 20.
• Multiply each score by the frequency. Add them together and
divide by N
CHARACTERISTICS OF THE MEAN
• Summed deviations about the mean equal 0.
• The mean is sensitive to extreme scores.
• The sum of squared deviations is least about the mean (pp. 8283).
Comparison of the Mean, Median, and Mode
• The mode is the roughest measure of central tendency and is
rarely used in behavioral statistics.
• Mean and median are generally more appropriate.
• If a distribution is skewed, the mean is pulled in the direction of
the skew. In such cases, the median is a better measure of
central tendency.
Why Measure Dispersion?
• Measures of dispersion tell us how spread out the scores in a
data set is. Surely all scores will not be equal to the mean.
• There are three measures of dispersion we will look at:
• Range (crude range)
• Variance
• Standard Deviation
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THE RANGE
The simplest measure of variability. Simply the highest score
minus the lowest score.
Limited by extreme scores or outliers.
THE VARIANCE
The sum of the squared deviations from the mean divided by N.
Calculating Variance (Deviation Formula)
Calculating Standard Deviation
Simply calculate the square root of the variance.
• So if s2 from the previous example was 3.11, the standard
deviation (denoted by s) is 1.76.
EXERCISE
• CALCULATE
MEAN, MODE, MEDIAN, RANGE, VARINCE AND STANDARD
DEVIATION OF FOLOWING DATA.
• (2,3,3,2,4,5,6,4,7,5,1,3,2,8,9,10,3,4,3,11).
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