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Prepared By: Dr.Anees AlSaadi
Community Medicine Department
December 2013
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Data Summarization Descriptive statistics:
• Continuous Data Description:
– Measures of Data Center :
• Mean, Median and Mode / definition.
• Practical Exercise.
– Measures of data variability:
• Standard deviation(variance)/ Range.
• Practical Exercise.
– Normal Distribution Curve.
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Measures of Center:
• Synonyms:
– Measure of central tendency.
– Measures of location.
• Identification of the center of the distribution
of observations OR the middle or average or
typical value.
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Measures of Center:
Mean
• Arithmetic average for all
observations.
Median
• The middle observation of
ordered data.
Mode
• Most frequently observed
value(s)
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Measures of Center:
Sample Mean:
• The most commonly used
measure of location.
• Called Arithmetic average.
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Measures of Center:
How to Calculate Sample Mean:
• Add up data, then
divided by sample
size (n).
• (n) is the number of
observations.
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Measures of Center:
How to Calculate
Sample Mean Example:
These are systolic blood
pressure in (mmHg)
120,80,90,110,95.
X1 =120, X2 =80 … X5 =95
Mean is calculated by adding up
the five vales and dividing by 5.
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Measures of Center:
How to Calculate Sample Mean
‾
X= 120+80+90+110+95/5= 99mmHg.
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Measures of Center:
Sample Mean Example:
Calculate the sample mean for number of open heart
surgeries done by 7 cardiothoracic surgeons in
Hamad hospital during last moth. Where, Dr.A did 4,
Dr.B 3, Dr.C 6, Dr.D 5, Dr. E 4, Dr. F 3 and Dr.G 5.
4.28 surgeries.
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Measures of Center:
Sample Mean Example:
The most important feature of the mean is
sensitivity to the extreme values (outlier)
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Measures of Center:
Sample Median
Is the middle number also called 50th
percentile.
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Measures of Center:
How to Identify Sample Median
• Order observations from smallest to largest.
• Find the observation in the middle of the data.
• Median is the observation in the middle.
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Measures of Center:
How to Identify Sample Median
Sample Median Example:
Identify the median for the following set of
observations:
– 90,80, 200,95, 110.
95
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Measures of Center:
How to Identify Sample Median
Sample Median Example:
• Identify the median for the following set of
observations:
– 90, 80, 120, 95, 125, 110.
Position n+1/2
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Measures of Center:
Sample Median Features:
Not affected by the extreme values.
Less efficient to summarize the data statistically.
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Measures of Center:
Sample Mode
• The most commonly occurring value in
dataset.
• Not all datasets have a mode.
• Unimodal distribution: one mode in the
dataset.
• Bimodal distribution: two modes in the dataset.
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Measures of Center:
How to Identify Sample Mode
• Arrange the data from small to greater values.
• The most commonly / repeated value is the
sample mode.
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Measures of Center:
How to Calculate Sample Median
Sample Mode Example:
{15, 33, 65, 32, 78, 94, 33, 110, 11, 46, 33}
{11, 15, 32, 33, 33, 33, 46, 65, 78, 94, 110}
Mode is 33
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Measures of Center:
Sample Mode Feature
Not affected by the extreme values.
Less efficient to summarize the data statistically.
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Practical Exercise
This dataset is the number of hysterectomy
performed by female doctors in HMC;
{44, 37, 86, 50, 20, 25, 28, 25, 31, 33, 85, 59,
27, 34, 36}
find the mean, median and mode?
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Data Summarization Descriptive statistics:
• Continuous Data Description:
– Measures of Data Center :
• Mean, Median and Mode / definition.
• Practical Exercise.
– Measures of data variability (dispersion) :
• Standard deviation(variance)/Range/ Interquartile range.
• Practical Exercise.
– Normal Distribution Curve.
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Measures of Data Dispersion
• Data dispersion = data spread.
• Data dispersion:
– Range.
– Interquartile range.
– Variance.
– Standard Deviation.
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Measures of Data Dispersion
Range:
• Is equal to largest ( Maximum) value minus
smallest (Minimum) value.
• Easy to calculate but it gives no idea about the
values between the Max and Min.
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Measures of Data Dispersion
Range:
Range Example:
Calculate the range for the following dataset;
{40, 28, 42, 30, 31, 38,100, 20, 48, 50, 51, 30}
Range is 100-20=80
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Measures of Data Dispersion
Range Feature:
Range is affected by the extreme of values.
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Measures of Data Dispersion
Interquartile Range
• Quartiles: the 25th , 50th , 75th percentiles of
the data.
• Interquartile range is the distance between
the 25th and 75th percentile.
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Measures of Data Dispersion
Interquartile Range
Max
• Max, Min,, 1st ,
3rd quartiles and
median are used
to make box-plot
(five number
summary)
75th Percentile
Median
50th Percentile
25th Percentile
Min
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Measures of Data Dispersion
Interquartile Range
• Quartiles are number that divide the
dataset into four quarters with 25% of
observations in each quarter
• Q1 lower quartile 25% of observations
below and 75% above it.
• Q2 median and 50% observations on
each side of it.
• Q3 upper quartile 25% of
observations above and 75% below it.
Q3
Q2
Q1
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Measures of Data Dispersion
How to Find Interquartile Range
• Arrange the data from the smallest to the
largest.
• Divide the data into two parts.
• Define Q1 as the median of the lower half of
the data.
• Define Q3 as the median of the lower half of
the data.
• Interquartile range is the Q3-Q1.
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Measures of Data Dispersion
How to Find Interquartile Range
Interquartile Range Example:
{20, 28, 30, 30, 31, 38, 40, 42, 48, 50, 51, 100}
{20, 28, 30, 30, 31, 38, 40, 42, 48, 50, 51, 100}
Q1=25th percentile= 30
Q3=75th percentile= 49
Interquartile Range (IQR)= Q3-Q1=19
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Measures of Data Dispersion
Variance:
• Is the averaged squared deviation from the mean.
• The units of measurement are those of the original
data squared.
• Variance: S2 or ϭ2
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Measures of Data Dispersion
Standard Deviation:
• Best used when mean is used as measure of center.
• Standard Deviation = 0 indicates no spread all the
data have the same value.
• Is affected by extreme observations.
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Measures of Data Dispersion
Standard Deviation:
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Choosing Measures of Center and Spread
If the distribution
is normal or
symmetrical
• Use mean and standard deviation.
If the distribution
is skewed OR has
large outliers.
• Use Median and range OR (IQR)
If the distribution
is bimodal
• Use mode and range OR find out
if the two modes represent two
different groups and separate them
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Characteristics of Measures of Spread
Range
IQR
Standard Deviation
Simple
Resistance
Non-Resistance
Non-Resistance
Used with the median
Used with the mean
IQR = 0 does not mean
there is no spread
Good for symmetrical
distribution with no outliers
Standard deviation of 0
means there is no spread.
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