Basic statistics

Ms. Greeva Philip
Department of Statistics
Manipal University, Manipal
6/14/2018
1
INTRODUCTION TO BASIC STATISTICS

INTRODUCTION TO STATISTICS
• Statistics is a field of study concerned with
collection, organization, summarization and
analysis of data, and the drawing of inferences
about a body of data when only a part of the data
is observed
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INTRODUCTION TO STATISTICS
• Biostatistics- Statistical methods applied in the
field of biology
• Mainly we use statistics for research stuides
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STEPS IN RESEARCH STUDIES
1. Identifying the question/objective
2. Designing a Study
3. Collecting Data
4. Analyze the data
5. Make Conclusions and Discuss Limitations
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COMPONENTS THAT CAPTURE THE
ESSENCE OF STATISTICSARE LISTED
BELOW
1. Collection of data
2. Organization of data
3. Presentation of data
4. Summarization of data
5. Significance testing
6. Drawing inferences and Interpreting data
7. Finally, Communicating data
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• Population- It is an entire group of people or
study element-persons, things or measurements
for which we have an interest at a particular time.
• Parameter is a characteristic of population
• Sample- It can be defined as a part of population.
• Statistic is a characteristic of sample
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DATA
The raw material of Statistics is data.
• We may define data as figures. Figures result
from the process of counting or from taking a
measurement.
For example:
• When a hospital administrator counts the number
of patients (counting).
• When a nurse weighs a patient (measurement)
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SOURCES OF DATA
• Routinely kept records
• Surveys
• Experiments
• External Sources
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TYPES OF DATA
1. Primary data
The raw data which has just been collected
from the source and has not gone any kind of
statistical treatment like sorting and tabulation
2. Secondary data
Data which has already been collected by
someone, may be sorted, tabulated and has
undergone a statistical treatment.
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VARIABLE
 It is a characteristic that takes on different values
in different persons, places, or things
Example:
 Heart rate,
 The SBP of adult males,
 The BMI of preschool children,
 Eye color
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VARIABLE
 Qualitative variables- are categories which take on
values that are names or labels.
Examples; Hair color, gender, status of a disease, etc.
 Quantitative variables- whose values result from
counting or measuring something
Examples: Height, age, Cholesterol level, etc.6/14/2018
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QUANTITATIVE VARIABLE
1. Discrete Variable-Variable that can only take on
a finite number of values or a variable whose value
is obtained by counting.
Examples;
• Number of students present,
• Number of heads when flipping three coins,
• Number of daily admissions in a hospital.
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QUANTITATIVE VARIABLE…
2. Continuous variable- Variable that has an
infinite number of possible values or variable
whose value is obtained by measuring
examples;
• Height and weight of students
• Hemoglobin level of adults
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QUALITATIVE VARIABLE
• Nominal variable- A variable with values which have
no numerical value. These have two or more
categories without having any kind of natural order.
Examples; Gender, Marital status, etc.
• Ordinal Variable- A categorical variable for which
the possible values are ordered
examples; Educational level, status of a disease
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MEASURES OF CENTRAL TENDENCY
• It is a measure of concentration of all other
observations around the central value
• We are looking for the average value or center value
• It helps to find which group is better off by
comparing the average of one group with that of the
other
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MEAN
• It is sum of all observations divided by number of
observations
• Most familiar and widely used measure used to
summarize continuous variable
• It cannot be used for a qualitative variable
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MEAN…
• 𝑚𝑒𝑎𝑛 =
𝑡𝑜𝑡𝑎𝑙 𝑜𝑟 𝑠𝑢𝑚 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠
• 𝑚𝑒𝑎𝑛 =
𝑋1+𝑋2+⋯+𝑋𝑛
𝑛
, = 𝑖=1
𝑛 𝑋 𝑖
𝑛
• where 𝑛 𝑖𝑠 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠 and X can
be weight, height, Hb level etc…
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MEDIAN
• It is the middle most value of the array arranged in
increasing or decreasing order of magnitude
• It is a value that is greater than 50% of observations
and lesser than remaining 50% of the observations
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MEDIAN…
• When ‘n’ is odd
Median is the middle observation in the ordered
sequence
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MEDIAN…
• When n is even
Median is the mean of the two middle observations in
the ordered sequence
(median=average(add the two middle numbers and
divided by two))
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MODE
• Mode is a value of the variable which occur more
frequently
Eg: No of children per family
0,1,0,1,4,2,1,1,2,1,0,1,2,1
mode is 1
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MEASURES OF DISPERSION
Measure of dispersion, conveys information
regarding the amount of variability present in a set
of data
Commonly used measures of dispersion include:
1. Range
2. Variance
3. Standard deviation
4. Mean Deviation
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MEASURES OF DISPERSION…
 Range- range is the difference between the smallest
and largest value in a set of observations.
𝑅 = 𝑋 𝐿 − 𝑋𝑆
 Where, R is Range, 𝑋 𝐿 is the largest value and 𝑋𝑆 is
the smallest value in a set of observation.
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Example,
The range of the numbers
1, 2, 4, 6,12,15,19, 26
= 26 -1
= 25
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Variance
 A measure of how far a set of numbers are spread
out from each other.
 It describes how far the numbers lie from the
mean
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 
1
1
2
2





n
xx
s
n
i
i

Standard Deviation(SD)
 Square root of variance is known as Standard
Deviation
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 
1
1
2




n
xx
s
n
i
i

MEASURES OF DISPERSION
Mean Deviation
 Mean deviation (MD) of a data set is
the average of absolute distance between each
data value and the mean
 Mean Deviation =
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n
xx 

REFERENCES
• Parks text book of ‘Preventive and Social Medicine’
• Mahajan’s ‘Methods in Biostatistics for Medical
Students and Research Workers’
• ‘Biostatistics’ by Wayne Daniel
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Basic statistics

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