This document discusses descriptive statistics and how they are used to summarize raw data. Descriptive statistics include rates, ratios, proportions, measures of central tendency (mean, median, mode), variation (standard deviation), and position (percentiles, quartiles). These statistics can be presented numerically and graphically using tables, bar charts, pie charts, histograms, box plots, and scatter plots. Software like MS Excel is commonly used to calculate descriptive statistics and generate graphs to meaningfully reduce and present large amounts of raw data.

1. Descriptive Statistics
Dr. A.P. Kulkarni

2. Necessity
Required for inference
Meaningful reduction
Raw data reduced
Depends on variable
Availability of software

3. What descriptive stats?
Rate
• Numerator,
denominator &
multiplier
• Has reference
period (Usually
year)
• Example: Crude
birth rate, Crude
death rate
CBR
• Numerator: Live
births
• Denominator: MYP
• Multiplier: 1000
• Reference period:
Year

4. What descriptive stats?
Ratio
• Mathematical
relation of
numerator with
denominator
• Denominator does
not include
numerator
• Example: A / B
• B does not include A
• May have multiplier
Example
• Sex ratio
• F * 1000/M

5. What descriptive stats?
Proportion
• Relation of
numerator with
denomianator
• Denominator
includes numerator
• Example: A/(A+B)
• May have
multiplier
Cure rate
• Cured *100 /
(Cured +Not
cured)
Case Fatality Rate
Died *100/ (Died +
Survived)

6. What descriptive stats?
Nominal & Ordinal
• Count
• Proportion (%)
Interval & Ratio
• Minimum
• Maximum
• Centering Const
• SD
• Percentiles
• Box-plot

7. What descriptive stats?
Nominal & Ordinal
Count
• Absolute number
of individuals with/
without
characteristic of
interest
Example
Number of
individuals cured /
not cured
Number of males/
females
Display
Table, Graph

8. What descriptive stats?
Interval / ratio scale
Minimum & Maximum
• Minimum / Maximum value
Example
• Minimum & maximum height in the group
• Used to ascertain that inclusion / exclusion
criteria are followed

9. What descriptive stats?
Interval / ratio scale
Centering constants: Mean, Median, Mode
• Mean: Arithmetic mean.
• Median: Middle value when arranged in
ascending / descending order
• Mode: Most common value
• Used to compare groups
• Mean is most commonly used statistics
• Limitations of Mean

10. What descriptive stats?
Interval / ratio scale
Standard deviation:
• Measure of variation.
• Has the same unit of measurement as mean
• Higher the SD higher is the variation in the
data
• Can compare two groups
• Required for further statistics
• Variance is square of SD

11. What descriptive stats?
Interval / ratio scale
Quartiles
• Measure of variation.
• Observations arranged in ascending order
• If there are 500 observations,
125th observation indicates 1st quartile (Q-1)
250th observation indicates 2nd quartile (Q-2)
375th observation indicates 3rd quartile (Q-3)

12. What descriptive stats?
Interval / ratio scale
Percentile:
• Measure of variation.
• Observations arranged
in ascending order
• If there are 500
observations, 5th
observation indicates
1st percentile,
• 475th observation is 95th
percentile
• Used in studies
related to
nutrition,
education,
psychiatry
• 50th percentile is
median

13. What descriptive stats?
Interval / ratio scale
Coefficient of Variation:
• SD divided by mean.
• May be expressed as %
• Useful to compare variables with different
units of measurement
• Example:
 Is height more variable or weight?
 Is Hb% more variable or ESR?

14. BOX PLOT
• Graphical
presentation of
Quantitative
variable
• Can be drawn with
help of software
• Lot of information
in one graph

15. What descriptive stats?
Interval / ratio scale
Skeweness & NORMAL
distribution:
• To decide if distribution is
Normal or not
• Types
• Skewed to right (+ve)
• Skewed to Left (-ve)
• It can be quantified
• Tests presuming normal
distribution not apllicable

16. Tables & Descriptive Statistics
What do tables
present
Counts Vs Characteristic
Number of persons
with characteristic
Groups:
Di-chotomous
Poly-chotomous
• How many
groups?
K = 1+ (3.332 x Log
10 (n))
K Number of
categories
N = number of
observations
•

17. Tables & Descriptive Statistics
2 by 2 table
Count of a variable in 2 groups
Gender Group Total
Study Control
M 60 64 124
F 40 36 076
Total 100 100 200

18. Tables & Descriptive Statistics
2 by 2 table
• Count of a 2 variables in 2 groups
• Showing association
Tuberculin Lepromin Total
+ (ve) (-) ve
(+) ve 189 011 200
(-) ve 023 377 400
Total 212 388 600

19. Tables & Descriptive Statistics
Frequency distribution table
• Frequency of categories in or more groups
• More than 2 categories/ 1 or more groups
Blood
Group
Cancer stomach Control
group
A
B
AB
O

20. Graphs in Describing Data
Qualitative data
Bar chart
Pie chart
Pictogram
Quantitative data
 Box plot
 Scatter chart
 Histogram
Depending on
objective
 Trend: Line chart
Correlation:
Scatter diagram

21. Bar Chart
Distribution of blood groups in donors
300
318
222
160
0
50
100
150
200
250
300
350
A B AB O

22. Pie Chart
Distribution of blood groups in donors
300
318
222
160
A
B
AB
O

23. Histogram

24. Scatter diagram

25. Line Diagram

26. Soft ware in descriptive statistics
MS-EXCEL
Master chart
Rows: Records
Columns: Variable
Coding the Qualitative variables
Use of functions
Export to other software like SPPSS