Data Display and Summary

1. Data Display and
Summary
Biostatistics
By Dr Zahid Khan

2. Data
• Data is a collection of facts, such as values or
measurements.
OR
• Data is information that has been translated into a
form that is more convenient to move or process.
OR
• Data are any facts, numbers, or text that can be
processed by a computer.
2

3. Statistics
Statistics is the study of the collection, summarizing,
organization, analysis, and interpretation of data.
3

4. Vital statistics
Vital
statistics
is
collecting, summarizing, organizing, analysis, presentation,
and interpretation of data related to vital events of life as
births, deaths,
marriages, divorces,
health & diseases.
4

5. Biostatistics
Biostatistics is the application of statistical techniques to
scientific research in health-related fields, including
medicine, biology, and public health.
5

6. Descriptive Statistics
The term descriptive statistics refers to statistics
that are used to describe. When using descriptive
statistics, every member of a group or population is
measured. A good example of descriptive statistics is
the Census, in which all members of a population are
counted.
6

7. Inferential or Analytical Statistics
Inferential statistics are used to draw conclusions and make
predictions based on the analysis of numeric data.
7

8. Primary & Secondary Data
• Raw or Primary data: when data collected having
lot of unnecessary, irrelevant & un wanted
information
• Treated or Secondary data: when we treat &
remove this unnecessary, irrelevant & un wanted
information
• Cooked data: when data collected not genuinely and
is false and fictitious
8

9. Ungrouped & Grouped Data
• Ungrouped data: when data presented or observed individually. For example if we observed
no. of children in 6 families
2, 4, 6, 4, 6, 4
• Grouped data: when we grouped the identical data by frequency. For example above data of
children in 6 families can be grouped as:
No. of children
Families
2
1
4
3
6
2
or alternatively we can make classes:
No. of children
Frequency
2-4
4
5-7
2
9

10. Variable
A variable is something that can be changed, such as a
characteristic or value. For example
age, height, weight, blood pressure etc
10

11. Types of Variable
Independent variable: is typically the variable representing the
value being manipulated or changed. For example smoking
Dependent variable: is the observed result of the independent
variable being manipulated. For example ca of lung
Confounding variable: is associated with both exposure and
disease. For example age is factor for many events
11

12. Categories of DATA
12

13. Quantitative or Numerical data
This data is used to describe a type of information
that can be counted or expressed numerically
(numbers)
2, 4 , 6, 8.5, 10.5
13

14. Quantitative or Numerical
data (cont.)
This data is of two types
1. Discrete Data: it is in whole numbers or values and has no
fraction. For example
Number of children in a family
= 4
Number of patients in hospital
= 320
2. Continuous Data (Infinite Number): measured on a
continuous scale. It can be in fraction. For example
Height of a person
=
5 feet 6 inches 5”.6’
Temperature
=
92.3 °F
14

15. Qualitative or Categorical data
This is non numerical data as
Male/Female,
Short/Tall
This is of two types
1.
Nominal Data: it has series of unordered categories
( one can not √ more than one at a time) For example
Sex
2.
=
Male/Female
Blood group = O/A/B/AB
Ordinal or Ranked Data: that has distinct ordered/ranked categories.
For example
Measurement of height can be = Short / Medium / Tall
Degree of pain can be = None / Mild /Moderate / Severe
15

16. Stem and Leaf Plots
• .Simple way to order and display a data set.
• Abbreviate the observed data into two significant digits.
0.6
Stem
• 0
• 1
• 2
• 3
2.6
0.1
Leaf
6 1
1 3
6 2
2
1.1
0.4
1.3
1.5
2.2
2.0
3.2
4
5
0
16

17. Measures of Central Tendency &
Variation (Dispersion)
17

18. Measures of Central Tendency
are quantitative indices that describe the center of
a distribution of data. These are
• Mean
• Median
• Mode
(Three M M M)
18

19. Mean
Mean or arithmetic mean is also called AVERAGE and only calculated
for numerical data. For example
• What average age of children in years?
Children
1234567
Age
6443246
-X = ∑X
___
n
Formula
Mean = 6 4 4 3 2 4 5 = 28
7
7
= 4 years
19

20. Median
• It is central most value. For example what is central value
in 2, 3, 4, 4, 4, 5, 6 data?
• If we divide data in two equal groups 2, 3, 4, 4, 4, 5, 6
hence 4 is the central most value
• Formula to calculate central value is:
Median = n + 1 (here n is the total no. of value)
2
Median = (n + 1)/2 = 7 + 1 = 8/2 = 4
20

21. Mode
• is the most frequently (repeated) occurring value in set
of observations. Example
• No mode
Raw data:
10.3 4.9 8.9 11.7 6.3 7.7
• One mode
Raw data:
2 3 4 4 4 5 6
• More than 1 mode
Raw data:
21 28 28 41 43 43
21

22. Comparison of the Mode, the
Median, and the Mean
• In a normal distribution, the mode , the median, and the
mean have the same value.
• The mean is the widely reported index of central
tendency for variables measured on an interval and ratio
scale.
• The mean takes each and every score into account.
• It also the most stable index of central tendency and thus
yields the most reliable estimate of the central tendency
of the population.

23. Histogram/Bar Chart
• Histogram & Box plots are used for continuous or
scale variables like temperature, Bone density etc
• Bar chart & Pie Charts are used to categorical or
nominal variables like gender, name etc.
23

24. Measures of Dispersion
quantitative indices that describe the spread of a data set.
These are
•
•
•
•
•
•
Range
Mean deviation
Variance
Standard deviation
Coefficient of variation
Percentile
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25. Range
It is difference between highest and lowest values
in a data series. For example:
the ages (in Years) of 10 children are
2, 6, 8, 10, 11, 14, 1, 6, 9, 15
here the range of age will be 15 – 1 = 14 years
25

26. Mean Deviation
This is average deviation of all observation from the mean
Mean Deviation = ∑ І X – X І
_______
_
n
here X = Value, X = Mean
n = Total no. of value
26

27. 27
Mean Deviation Example
A student took 5 exams in a class and had scores of
92, 75, 95, 90, and 98. Find the mean deviation for her test scores.
• First step find the mean.
_
x=∑x
___
n
= 92+75+95+90+98
5
= 450
5
= 90

28. • 2nd step find mean deviation
Values = X
ˉ
Mean = X
Deviation from
ˉ
Mean = X - X
Absolute value of
Deviation
Ignoring + signs
92
90
2
2
75
90
-15
15
95
90
5
5
90
90
0
0
98
90
8
8
Total = 450
n= 5
--
Mean Deviation
=
Dr. Riaz A. Bhutto
_
∑І X – X І
_______ = 30/5
n
∑ X - X = 30
=6
Average deviation
from mean is 6
9/3/2012
28

29. Variance
• It is measure of variability which takes into account
the difference between each observation and mean.
• The variance is the sum of the squared deviations
from the mean divided by the number of values in
the series minus 1.
• Sample variance is s² and population variance is σ²
29

30. Variance (cont.)
•
•
•
•
•
The Variance is defined as:
The average of the squared differences from the Mean.
To calculate the variance follow these steps:
Work out the Mean (the simple average of the numbers)
Then for each number: subtract the Mean and square the
result (the squared difference)
• Then work out the average of those squared differences.
30

31. 31
Example: House hold size of 5 families was recorded as following:
2, 5, 4, 6, 3
Step 1
Values = X
Calculate variance for above data.
Step 2
ˉ
Mean = X
Step 3
Step 4
Deviation from
ˉ
Mean = X - X
ˉ
( X – X)²
2
4
-2
4
5
4
1
1
4
4
0
0
6
4
2
4
3
4
-1
1
Step 6 =
Dr. Riaz A. Bhutto
s² =
_
∑ ( X – X)² = 10/5 = 2
_______
n
∑ = 10 Step 5
S²= 2 persons²
9/3/2012

32. Standard Deviation
• The Standard Deviation is a measure of how spread out numbers are.
• Its symbol is σ (the greek letter sigma)
• The formula is easy: it is the square root of the Variance.ie
s = √ s²
• SD is most useful measure of dispersion
s = √ (x - x²)
n
(if n > 30) Population
s = √ (x - x²)
n-1
(if n < 30) Sample
32

33. Standard Deviation and Standard
Error
• SD is an estimate of the variability of the
observations or it is sample estimate of population
parameter .
• SE is a measure of precision of an estimate of a
population parameter.