This document discusses data, scales of measurement, and measures of central tendency. It defines data as individual pieces of information used for analysis, and distinguishes between qualitative and quantitative data. There are four main scales of measurement - nominal, ordinal, interval, and ratio - which differ in their mathematical properties and appropriate statistical analyses. Measures of central tendency discussed include the mean, median, and mode, which provide a single value to represent the center of a data set.

1. DATA AND SCALES OF
MEASUREMENT
PRESENTED BY : DR. RITU
RANDAD
FIRST YEAR MDS
1

2. CONTENTS
• Introduction
• What is DATA and SCALE?
• Types of data
• Types of scales
• Measures of central tendencies
• Conclusion
• References
2

3. INTRODUCTION
• In our daily life we are said to measure or calculate various
information which determines weight, height or some other features
of a physical object. We also measure when we judge how well we
like a song, a painting or the personalities of people.
• We thus measure physical objects as well as abstract concepts. It is
easy to assign numbers in respect of properties of some objects,
but it is relatively difficult in respect of others. Like measuring
things as social conformity, intelligence or marital status.
Fava GA, Tomba E, Sonino N ,Clinimetrics: the science of
clinical measurements.
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4. • Properties like weight , height etc can be measured directly with
some standard of unit of measurement, but it is not easy to
measure properties like motivation to succeed, ability to stand and
so on.
• To indicate a domain concerned with indexes, rating scales and
other expressions that are used to describe
or measured symptoms, physical signs and other clinical
phenomena, we use various scales to measure them.
4
Mahajan’s methods in Biostatistics for medical students and research workers, Bartati Banerjee, 8th edition,
New Delhi.

5. WHAT IS A MEASUREMENT?
• Measurement is defined as a process of associating numbers or
symbols to observations obtained in a research study.
• These observations can be qualitative or quantitative.
5
Mahajan’s methods in Biostatistics for medical students and research workers, Bartati Banerjee,
8th edition, New Delhi.

6. WHAT IS DATA?
• Data are individual pieces of information recorded and used for
the purpose of analysis.
• It is the raw information from which statistics are
created. Statistics are the results of data analysis - its
interpretation and presentation.
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C R Kothari, Research Methodology methods and techniques, 3rd

7. • Data is distinct pieces of information, usually formatted in a
special way. Data can exist in a variety of forms — as numbers or
text on pieces of paper, as bits and bytes stored in electronic
memory, or as facts stored in a person's mind.
• Data is the plural of datum, a single piece of information. In
practice, however, people use data as both the singular and
plural form of the word, and as a mass noun.
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8. • Data provides facts and figures from which conclusions can be
drawn.
• Data can relate to an enormous variety of aspects.
1. Weight and height recorded of students in a class.
2. Blood pressure and pulse rate recorded of patients in a
medical opd.
3. Temperature of a city for a week.
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9. • The data collected may be for
profile or prospective studies at
local, state, national or
international levels.
• Used to analyze changes in
health or disease situations in
community or population by
standard parameters.
Quantitative
Qualitative
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C R Kothari, Research Methodology methods and techniques, 3rd

10. QUANTITATIVE DATA
• Quantitative Data: Data that can
be measured with numbers,
such as time, weight, number of
participants, Number of defects,
effort required to complete the
task. It is called Numerical data.
QUALITATIVE DATA
• Qualitative data: Data can be
represented by a name, symbol,
or a number code. It is called
Nonnumerical data that is
usually textual and descriptive
like female, most favorite,
yes/no.
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C R Kothari, Research Methodology methods and techniques, 3rd
edition, Jaipur

11. QUALITATIVE DATA
• There is no notion of magnitude or size of attribute, hence the
presentation of frequency distribution is simple because the
characteristic is not variable but discrete.
• Classified by counting the individuals having same
characteristic or attribute and not by measurement.
• Only one variable is used.
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C R Kothari, Research Methodology methods and techniques, 3rd

12. • Qualitative data also called as categorical data since this data can be
grouped according to categories.
• Qualitative data does not include numbers in its definition of traits.
• Qualitative data is about the emotions or perceptions of people, what
they feel.
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13. 13
Qualitative data is important in
determining the frequency of
traits or characteristics. It allows
the statistician or the researchers
to form parameters through
which larger data sets can be
observed.
Qualitative data provides the
means by which observers can
quantify the world around them.

14. METHODS OF
COLLECTING
QUALITATIVE
DATA
1. One on one
interview (face to
face interview)
2. Focus groups
3. Record keeping
4. Process of
observation
5. Longitudinal
studies
6. Case studies
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15. ADVANTAGES
1. In helps in depth
information and analysis.
2. Rich data.
3. Understands what the
customer/ patient thinks.
DISADVANTAGES
1. Time consuming
2. Result depends on what
researcher thinks.
3. Not easy to generalize.
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16. QUANTITATIVE DATA
• Quantitative data is defined as the value of
data in the form of counts or numbers where
each data-set has a unique numerical value
associated with it. This data is any
quantifiable information that can be used for
mathematical calculations and statistical
analysis, such that real-life decisions can be
made based on these mathematical
derivations.
• This data can be verified and can also be
conveniently evaluated using mathematical
techniques.
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17. • Quantitative data makes measuring various parameters
controllable due to the ease of mathematical derivations they
come with. Quantitative data is usually collected for statistical
analysis using surveys, polls or questionnaires sent across to a
specific section of a population. The retrieved results can be
established across a population.
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18. • Quantitative data is any quantifiable
information that can be used for
mathematical calculation or statistical
analysis. This form of data helps in
making real-life decisions based on
mathematical derivations.
• This data can be validated and verified.
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19. QUANTITATIVE DATA
• The data have a magnitude.
• The characteristics is measured
either on an interval or on ratio
scale.
• There are two variables : as
height and frequency , eg:
number of person with same
characteristic and in same range.
19C R Kothari, Research Methodology methods and techniques, 3rd
DISCRETE
CONTINOUS

20. TYPES OF QUANTITATIVE DATA
1. Counter
2. Measurement of physical objects
3. Sensory calculations
4. Projection of data
5. Quantification of qualitative entities.
Surveys and interviews are the main source to collect
quantitative data.
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21. ADVANTAGES
1. Conduct in depth
interviews.
2. Minimal bias
3. Accurate results
DISADVANTAGES
1. Resisted information
2. Depends on question types
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22. EXAMPLES OF
DATA
22https://www.google.com/search?q=examples+of+qualitative+data&sxsrf=ALeKk01QDaa9e2N60XBZlB9HgCDaoYF_9g:
1590085060787&source=lnms&tbm=isch&sa=X&ved=2ahUKEwiVxde5yMXpAhU7gUsFHdCTCkIQ_AUoAXoECBEQAw#im

23. DISCRETE DATA
• Information that can be categorized into a classification.
• Discrete data is based on counts. Only a finite number of value
are possible, and the values that cannot be subdivided
meaningfully.
• Attribute data (discrete data) is data that can’t be broken down
into a smaller unit and add additional meaning. It is typically
things counted in whole numbers. There is no such thing as
half a defect
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24. CONTINUOUS DATA
• Information that can be measured on a continuum or scale.
Continuous data can have almost any numeric value and can be
meaningfully subdivided into finer and finer increments,
depending upon the precision of the measurement system.
• Continuous data can be recorded at many different points (length,
size, width, time, temperature, cost, etc.).
• Continuous data is data that can be measured and broken down
into smaller parts and still have meaning. Temperature and time,
volume (like volume of water or air) and size are continuous data.
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25. WHAT IS SCALE?
• A scale is a tool or mechanism by which individual are distinguished
as to how they differ from one another on the variables of interest to
our study.
• The scales of measurements can be considered in terms of their
mathematical properties.
• a) nominal scale
• b) ordinal scale
• c) interval scale
• d) ratio scale 25
Mahajan’s methods in Biostatistics for medical students and research
workers, Bartati Banerjee, 8th edition, New Delhi.

26. TYPES OF SCALES
a) nominal
scale
b) ordinal
scale
c) interval
scale
d) ratio
scale
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28. NOMINAL SCALE/ COUNTED DATA
• Nominal scale is simply a system of assigning numbers or symbols to events
in order to label them.
• The numbers are just convenient labels for the particular class of events and
as such have no quantitative value.
• They help in keeping tracks of events, people and objects.
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Mahajan’s methods in Biostatistics for medical students and research
workers, Bartati Banerjee, 8th edition, New Delhi.

29. NOMINAL SCALE
• Nominal data/scale is a type of data
that is used to label variables
without providing any quantitative
value. Qualitative characteristics can
be counted but not computed.
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Mahajan’s methods in Biostatistics for medical
students and research workers, Bartati Banerjee, 8th

30. • For recording the acquired data of marital status as 1,2,3 or 4
depending upon whether the person is single, married,
widowed or divorced.
• We can also record the characteristic has “yes or no” answers to
question as “0” or “1”.
30
Mahajan’s methods in Biostatistics for medical
students and research workers, Bartati Banerjee, 8th

31. • In the artificial or nominal way, categorical data can be made
into numerical data , we refer these numbers we record as
nominal data.
• Nominal data is numerical in name only , because they don’t
share any of the properties of numbers we deal in ordinary
arithmetic.
• The numbers used are just a convenient labels for the
particular class of events and as such have no quantitative
value.
31
Mahajan’s methods in Biostatistics for medical
students and research workers, Bartati Banerjee, 8th

32. The nominal scale is the least powerful level of measurement. It
indicates no order or distance relationship and no arithmetic origin.
It simply describes the differences between things by assigning them
to categories.
They are widely used in surveys when data is being classified by
major sub-groups of the population.
Examples: - gender
- race
-whether or not tumor recurred
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Mahajan’s methods in Biostatistics for medical students and research workers,
Bartati Banerjee, 8th edition, New Delhi.

33. ORDINAL SCALE
• The lowest level of the ordered scale that is commonly used .
• This place events in order, but there is no attempt to make the
intervals of scales equal in terms of rule.
• They are generally used in research related to qualitative
phenomena.
• Ordinal data only permits the ranking of items from highest to
lowest.
33
Mahajan’s methods in Biostatistics for medical students and research workers, Bartati
Banerjee, 8th edition, New Delhi.
Principles and practices of Biostatistics, B. Antonisamy, 10 July 2017, 7th edition.

34. ORDINAL SCALE
• In situations when we can not do anything except set
up inequalities, we refer to data as Ordinal data.
• For example, one mineral can scratch another, it
receives a higher hardness number on scale from 1 to
10. with this numbers we can write 5>2 or 6<9 , but
we cannot write as 5-2 = 6-9.
• The greater than symbol (>) in connection with ordinal
data may be used to designated “happier than” or so
on.
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Mahajan’s methods in Biostatistics for medical students and research
workers, Bartati Banerjee, 8th edition, New Delhi.

35. The use of ordinal data implies a statement of
“greater than ” or “less than” without being able to
state how much greater or less.
The appropriate measure of central tendency is the
median.
They have no absolute values, and real differences
between ranks may not be equal.
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36. INTERVAL SCALE
• The interval are adjusted in terms of rule that establishes on a
basis for making the unit equal.
• They have an arbitrary zero, but they are not possible to
determine for an absolute zero or the unique origin.
• The primary limitation is lack of true zero, it does not have a
capacity to measure the complete absence of a trait or
characteristic.
36
Principles and practices of Biostatistics, B. Antonisamy, 10 July 2017,
7th edition.

37. INTERVAL DATA
• Interval data, also called an integer, is defined as a data type
which is measured along a scale, in which each point is placed
at equal distance from one another. Interval data always
appears in the form of numbers or numerical values where the
distance between the two points is standardized and equal.
37
Mahajan’s methods in Biostatistics for medical
students and research workers, Bartati Banerjee, 8th

38. • When in addition to setting up
inequalities we can also form
differences.
• For eg: for following temp
reading 58˚, 63˚,
70˚,95˚,126˚. In this we can
write as 126˚> 70˚or 58˚ <
95˚ which simply means that
126˚ is warmer than 70˚ or 58˚
is cooler than 95˚.
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Mahajan’s methods in Biostatistics for medical
students and research workers, Bartati Banerjee, 8th

39. • Interval scales are powerful measurement as it incorporates the
concept of equality of interval.
• Mean is the appropriate measure of central tendency , while
standard deviation is mostly used as measure of dispersion.
39
Principles and practices of Biostatistics, B. Antonisamy, 10 July 2017, 7th

40. Examples are : -temperature (o does
not mean no heat at all)
:- calendar dates
:- IQ scores (o does not mean no
intelligence at all)
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41. RATIO SCALE
• Ratio scales have an absolute or true zero of measurement. Eg:
zero point on scale of centimeter indicates the
complete absence of length or height.
• Ratio scales represents the actual amount of variables.
• Multiplication and divisions can be used with this scale.
• Examples : duration, mass, length, energy and electric
charge.
CC R Kothari, Research Methodology methods and techniques, 3rd
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42. RATIO DATA
• Ratio Data is defined as a
quantitative data, with an equal
and definitive ratio between
each data and absolute “zero”
being treated as a point of
origin. In other words, there can
be no negative numerical value
in ratio data.
• In this sense, ratio data includes
all the usual measurement of
length, height, money amounts,
weight, volume, area, pressures
etc.
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Mahajan’s methods in Biostatistics for medical students and research workers, Bartati
Banerjee, 8th edition, New Delhi.

43. MEASURES OF CENTRAL TENDENCY-
AVERAGES
• Information from a series of observations is summarized by an
observer to get answers
• Average value of a characteristic is the one central value around
which all other observations are dispersed.
• In larger series, nearly 50% observations lie above while 50%
remains below the central value.
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C R Kothari, Research Methodology methods and techniques, 3rd
edition, Jaipur

44. • Central value helps 1) to find which group of the normal observation lie
close to central value, while few others of the too large or too small lie
far away at both the ends.
• 2) to find which group is better off by comparing the
average of one group with that of the other
• Average is a general term which describes the center of the series.
1. MEAN
2. MEDIAN
3. MODE
4. STANDARD DEVIATION
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C R Kothari, Research Methodology methods and techniques, 3rd
edition, Jaipur

45. MEAN
•
This measure implies arithmetic average or arithmetic mean which is obtained by
summing up all the observations and then dividing the total by the number of
observation.
it is one central value, most usually used in statistical methods.
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C R Kothari, Research Methodology methods and techniques, 3rd

46. MEDIAN
• When all the observations are
arranged in either ascending
or descending order, the
middle observation is known
as median.
• It implies the mid value of the
series.
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C R Kothari, Research Methodology methods and techniques, 3rd

47. • Median, therefore, is a better indicator of central value when
one or more of the lowest or the highest observations are wide
apart or not so evenly distributed.
47

48. MODE
• This is the most frequently
occurring observation in a
series, that is most
common or most
fashionable.
• Mode is rarely used in
medical studies.
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C R Kothari, Research Methodology methods and techniques,
3rd edition, Jaipur

49. STANDARD DEVIATION
• The standard deviation is a measure
of the amount of variation or
dispersion of a set of values. A low
standard deviation indicates that the
values tend to be close to the mean
of the set, while a high standard
deviation indicates that the values
are spread out over a wider range.
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50. GOODNESS OF MEASUREMENT SCALES
• Certain characteristics are:
a) Validity: content validity and criterion-related validity
b) Relevance: (judged to be proper measure)
c) Freedom from bias: (equal opportunity)
d) Reliability: (criterion is stable/ reproducible)
e) Availability: (information must be available)
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51. CONCLUSION
Data type is an important concept of statistics, which should be
understood to implement statistical methods or procedures
correctly. Proper knowledge of data types is necessary to analyze
data sets with appropriate statistical methods.
Two types of measures : qualitative and quantitative
4 types of scales : nominal, ordinal, interval and ratio
Measurement scales : comparative and non-comparative scales.
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52. 52
QUANTITATIVE
DATA QUALITATIVE DATA
DISCRETE CONTINOUS
NON-
NUMERICAL
RATIO SCALE
NOMINAL SCALE ORDINAL SCALE
INTERVAL SCALE

53. REFERENCES
• Mahajan’s methods in Biostatistics for medical students and
research workers, Bartati Banerjee, 8th edition, New Delhi.
• Principles and practices of Biostatistics, B. Antonisamy, 10 July
2017, 7th edition.
• Fava GA, Tomba E, Sonino N ,Clinimetrics: the science of
clinical measurements.
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