Measures in Statistics and Basics of Data

1. Introduction to
Statistics
By;
Mr. Johny Kutty Joseph
Asstt. Professor

2. Concepts & Definition
• It is to organize, interpret, and communicate
numeric information.
• Logical thinking is required more than
mathematical ability.
• The word statistics comes from the Italian
words Statista means Statement and a
German word Statistik means political state..
• It is a science of learning from
numbers/data.
• It is a science of collecting, classifying,
analyzing and interpreting the data.

3. Concepts & Definition
• A branch of mathematics dealing with the
collection, analysis, interpretation, and
presentation of masses of numerical data.
(Merriam-Webster)
• Statistics is defined as collection,
Presentation, analysis and interpretation
of numerical data”. ( Croxton & Cowden)
• It is the sciences and art of dealing with
figure and facts.

4. Uses of Statistics
• To make the raw data meaningful.
• To test null hypothesis.
• To test the statistical significance of data .
• To draw inferences and make the
generalization.
• To estimate parameters.
• Make decisions based on data, and make
predictions.
• It helps in comparison

5. Biostatistics
• Biostatistics is the branch of statistics
applied to biological or medical sciences.
• Biostatistics is the methods used in
dealing with statistics in the field of
health sciences such as biology, medicine,
nursing, public health etc.
• Biostatistics is the branch of statistics
applied to biology or medical sciences.
Biostatistics is also called “Biometry”

6. Data
• Data is defined as factors known or assumed as
facts, making the basis of reasoning or calculation.
• Broadly there are quantitative and qualitative
data.
• Quantitative data deals with numbers and things
you can measure objectively: Eg; height, weight,
length, temperature, volume, area etc. It is
number value.
• Qualitative data deals with characteristics and
descriptors that can't be easily measured, but can
be observed subjectively. Eg. smells, tastes,
textures, attractiveness, and color.

7. Data
• Quantitative data; continuous and discrete.
• Discrete data is a count that can't be made
more precise. For instance, the number of
children in your family is discrete data,
because you are counting whole, indivisible
entities: you can't have 2.5 kids.
• Continuous data could be divided and
reduced to finer and finer levels. Eg; Height
of children made more precise by Meters-
centimeters-millimeters and beyond. So
height is continuous data.

8. Data
• Qualitative data; It is also referred as attributable
data. Binary, Nominal (unordered) and Ordinal
(ordered) data.
• Binary data place things in one of two mutually
exclusive categories: right/wrong, true/false, or
accept/reject.
• Nominal Data: We assign individual items number
or category that do not have an implicit or natural
value or rank. (Gender: 1=male and 2= female)
• Ordinal Data: The items are assigned to categories
that have some kind of implicit or natural order.
Eg. "Short, Medium, or Tall." Rating from 1 to 5
on scale where 5 is most appropriate.

9. Scales of Measurement
• Measurement is the process of assigning
numbers or labels to objects, persons, states,
or events in accordance with specific rules to
represent quantities or qualities of attributes.
• We do not measure specific objects, persons,
etc., we measure attributes or features that
define them.
• It is a system of classifying measurements
according to the nature of the measurement
and the type of mathematical operations to
which they match.

10. Scales of Measurement

11. Data Classification in Science

12. Nominal Measurement
• The lowest level of measurement also referred as
categorical data.
• It represents characteristics. Eg. Gender,
Language, locality etc. Numerical values may be
given but do not have any mathematical meaning.
• It act as labels and hence changing order doesn’t
have any significance.

13. Ordinal Measurement
• It is the second level, in which the scores are
given in such a manner as the number increases
the status/condition also increases or upgrades.
• The limitation of this type of data is that
difference between all the 4 options are not
equally measurable or not known.
• It is mainly used to measure non numerical
features such as patient satisfaction, etc.
How often do you feel
back pain ?
No Pain: 1, Mild Pain: 2
Moderate: 3, Severe : 4

14. Interval Measurement
• An interval scale has the characteristics of an
ordinal scale.
• An interval scale permits use of measurement that
enables data to be placed at equally spaced
intervals in relation to the spread of the variable.
• This measurement has a starting and a
terminating point that is divided into equal space
intervals.
• The problem with interval values data is that
they don’t have a true zero.
What is the room temperature ?
a) -20 to -10; b) -10 to 0; c) 0 to 10 ; d) 10 to 20

15. Ratio Measurement
• It is the highest level of data.
• A ratio scale is a scale that measures in terms of
equal intervals and an absolute zero point of
origin. It has all the properties of nominal, interval
and ordinal.
• The bio-physiological characteristics such as age,
weight, height are examples.
• The variables that are measured either on interval
or ratio are considered continuous.
• Eg. It can easily be stated that one who weighs 80
kg is twice heavy as someone who weighs 40kg.

16. Comparison of levels
• The levels of measurement forms a hierarchy,
with ratio at the top and nominal at the base.
• The higher the level of measurement precise is the
data.
• It is possible to convert data to lower level but not
the reverse process.
• A ratio may be converted to ordinal but ordinal
cannot be ratio. Assess the weight of people
Ordinal Ratio
a. Below 50 a. 40 to 50
b.50 to 70 b. 50 to 60
c. Above 70 c. 60 to 70
d. 70 to 80
Some psychological
scales (Likert’s scale)
are considered ordinal
as well as interval.

17. Classification of Statistics
• Descriptive Statistics: It is the enumeration,
organization and graphical representation of
data. It helps to summarize the meaning of
data. Eg. Demographic variables.
• Inferential Statistics: It is also called as
sampling statistics. It is the inference of
conditions that exist in large set of
observations. Eg. Test the efficiency of a new
hypertensive drug on a particular
population.

18. Descriptive Statistics
• It is classified as the following
• Frequency distribution and graphical
presentation(measures of condensation).
• Measures of central tendency. (Mean,
Median, Mode)
• Measures of dispersion. (difference) Eg.
Range, Mean deviation, Standard deviation,
Quartile deviation
• Measures of relationship (correlation
coefficient, regression etc.)

19. Frequency Distribution
• A set of data can be described in terms of
three characteristics. Distribution of values,
central tendency and variability (dispersion
and relationship).
• Distribution of values or frequency
distribution are used to organize the
numeric data.
• It is a systematic arrangement of values from
lower to higher together with count of
number/frequency with which the value was
obtained.

20. Frequency Distribution
• Observe the below given table for anxiety
scores of 60 patients.
• Inspection of these numbers does not help
us to understand patients anxiety.
22 24 25 19 24 25 23 23 24 20
25 16 20 25 17 22 24 18 22 23
15 24 23 22 21 24 20 25 18 25
24 23 16 25 30 20 19 21 23 24
19 18 20 21 17 25 22 24 20 17
20 25 21 24 23 19 21 21 25 21

21. Frequency Distribution
• Frequency distribution consists of two parts;
observed values (X) and frequency (f). N is
the sample size.
• Scores are in order in a column and
corresponding frequencies in another.
• The sum of numbers in the frequency must
be equal to N. (Σf=N)
• See the following frequency distribution
table of the given patient’s anxiety scores
that gives clear understanding of the data.

22. Frequency Distribution
SCORE (X) Frequency (f) Percentage (%)
15 1 1.7
16 2 3.3
17 3 5.0
18 4 6.7
19 4 6.7
20 7 11.7
21 7 11.7
22 4 6.7
23 8 13.3
24 10 16.7
25 10 16.7
N = 60 = Σf Σ% = 100.0%

23. Tables
• It represents data in concise, systematic
manner from the masses of statistical data.
• Tabulation is the first step in data analysis.
• A table consist of table number, title,
contents, foot notes etc.
• Tables are broadly classified into
• A. Frequency distribution table
• B. Contingency Table
• C. Multiple response table
• D. Miscellaneous Table.

24. Tables
• Frequency
distribution tables: it
represents frequency
and percentage
distribution of the
collected information.
Usually the number of
classes vary between 3
to 8. Too many or too
few classes may fail to
reveal the salient
features of data.
Socio demographic Profile of
patients
Variables N = 60
F (%)
Age (years)
20 -40
41 - 60
18 (30.0)
42 (70.0)
Gender
Male
Female
Transgender
39 (65.0)
21 (21.0)
0 (0.0)
Marital Status
Married
Unmarried
Divorced
52 (86.7)
08 (13.3)
0
Locality
Urban
Rural
31 (51.7)
29 (48.3)

25. Tables
• Contingency tables: it represents frequency
distribution of two mutually exclusive nominal
variables simultaneously. It is also called as cross
tables. These tables could be 2x2, 2x3 and 3x3
depending on the number of variables. The number
of subjects in a cell is called as cell frequency.
These tables are usually used for Chi-square test.
Type of Ventilation and Bowel movements in patients
Bowel
Movements
Spontaneous
ventilation
Mechanical
Ventilation
Total
frequency
χ2 value
Present 391 (64.0) 32 (29.4) 423 45.87
df=1 (c-1)(r-1)Absent 220 (36.0) 77 (70.6) 297
Total 611 109 720 (N)

26. Tables
• Multiple response
table: It is used to
represent data
that are neither
exclusive nor
exhaustive. It is
used when “f”
exceeds “N”. It is
made to represent
the percentage
distribution.
Factors Contributing to sleep
deprivation among patients.
Factors N = 60
F (%)
Blood sampling 35 (58.3)
Diagnostic Tests 33 (55.0)
Medication 33 (55.0)
Vital Signs
monitoring
32 (53.3)
Noise 32 (53.3)
Bright Lights 30 (50.0)

27. Tables
• Miscellaneous Table: Table that represent
data other than frequency or percentage
distributions such as mean, median, mode,
SD etc.

28. Graphical Representation of Data
• It is most convenient and appealing way in
which statistical results may be presented.
• It gives an overall view of the entire data and
is visually attractive.
• It facilitates comparison.

29. Types of Graphs and Diagram
• Bar Diagram: Useful in displaying nominal
or ordinal data. It shows the visual
comparison of magnitude of a variable and
its frequency. It may either be prepared
vertically or horizontally.
• There are mainly three types of Bar diagram
such as simple, multiple and proportion bar
charts. See the following examples.

30. Types of Graphs and Diagram
72
28
0
10
20
30
40
50
60
70
80
Vegetarian Non vegetarian
Simple bar diagram showing dietary pattern of
people
Vegetarian
Non vegetarian

31. Types of Graphs and Diagram
60
14
26
40
30 30
0
10
20
30
40
50
60
70
Asia Africa Europe
Multiple bar diagram showing the percentage of
population and land.
Population
Land

32. Types of Graphs and Diagram
0
10
20
30
40
50
60
70
80
90
100
Population Land
60
40
14
30
26 30
Proportionate bar graph showing worlds
population and land area
Europe
Africa
Asia

33. Types of Graphs and Diagram
• Pie Diagram/ Sector
diagram: Useful to
present discrete data
such as age groups,
gender, etc in a
population. The input
must be in percentage.
Size of the angle is
calculated by the
formula class
frequency/total
observation x 360
degree.
32
40
8
20
Health Problems of the
old age in Jammu
Hypertensi
on
Diabetes
Arthritis
Sensory

34. Types of Graphs and Diagram
• Histogram: The most commonly used graphical
representation of grouped frequency.
• Variable characters of different group/class is on
the x axis and their respective frequencies on y
axis.
• Frequency of each group forms a column or
rectangle.
• The area of rectangle is proportional to the
frequency of the class interval.
• Eg: Age group
(years)
15-20 20-25 25-30 30-35 35-40
No. of males 15 20 40 60 50

35. Types of Graphs and Diagram

36. Types of Graphs and Diagram
• Frequency Polygon: It is the curve (two
dimensional) obtained by joining the middle top
points of the rectangles in a histogram by straight
lines.
• The two end points of the line drawn are joined to
the x axis at the midpoint of the empty class
intervals.
• It is more simple and sketch the outline of the
data clearly than histogram.
• Eg
Age group
(years)
15-20 20-25 25-30 30-35 35-40
No. of males 15 20 40 60 50

37. Types of Graphs and Diagram
0
15
20
40
60
50
00
10
20
30
40
50
60
70
15 - 20 20 - 25 25 - 30 30 - 35 35 - 40
Number of Males
Number of Males

38. Types of Graphs and Diagram
• Line graph: In this the frequency polygon are
depicting by line.
• Commonly used to represent those data that is
collected over a long period of time.
• On x axis independent variables are presented
and dependent variables on the y axis.
• The plotted data can be joined by a straight lines.
Year 2001 2002 2003 2004 2005 2006 2007
Cars sold in
Delhi (in
thousand)
123 203 328 298 337 417 486
Cars sold in
Mumbai(in
thousand)
456 402 387 347 342 307 298

39. Types of Graphs and Diagram
123
203
328
298
337
417
486
456
402 387
347 342
307 298
0
100
200
300
400
500
600
2001 2002 2003 2004 2005 2006 2007
Line graph presenting the number of cars sold in
Delhi and Mumbai during 2001 - 2007
In Delhi
In Mumbai

40. Types of Graphs and Diagram
• Cumulative Frequency curve/ “ogive”: It is the
representation of cumulative frequency for
statistical purpose.
• First convert the frequency table to cumulative
frequency and then plot it on the line.
• It is also called as “ogive”.
Age group
(years)
15-20 20-25 25-30 30-35 35-40
No. of males 15 20 40 60 50
Cumulative
Frequency
15 35 75 135 185

41. Types of Graphs and Diagram
15
35
75
135
185
0
20
40
60
80
100
120
140
160
180
200
15 - 20 20 - 25 25 - 30 30 - 35 35 - 40
Number of Males
Number of Males

42. Types of Graphs and Diagram
• Scattered or dotted
diagrams: It is a
graphic representation
shows the nature of
correlation between
two variables. Eg.
Student marks in an
examination
• It is also called as
correlation diagram.
• It may be positive
(upward) or negative
(downward)
Number of
students
Marks
obtained out
of 100
12 40-50
10 50-60
8 60-70
7 70-80
5 80-90
2 90-100

43. Types of Graphs and Diagram
0
2
4
6
8
10
12
14
0 50 100 150
Numberofstudents
Marks obtained out of 100
Scattered diagram show the negative
correlation
No. of students

44. Types of Graphs and Diagram
• Pictograms or picture diagram: Use of pictures
to plot the frequency of a characteristics.
• Map diagram or spot map: Maps are prepared
to show geographical distribution of frequencies
of characteristics.

45. Limitations of Graphs
• It is confusing (depend on the type)
• It presents only quantitative data.
• It gets only on one aspect or on limited
characteristics.
• It can present only approximate values.