INTRODUCTION OF STATISTICS FINAL YEAR VIII SEM

INTRODUCTION OF
STATISTICS
Akshata A. Jain
Asst.prof.
KYDSCT’s College of
Pharmacy

INTRODUCTION
STATISTICS:
Statistics is the science which deals with the methods of collecting, classifying,
presenting, comparing, and interpreting numerical data collected in any sphere if
inquiry.
Knowledge on statistical concepts is desired for the development, production,
evaluation and marketing of various pharmaceutical dosage forms.
➤ Statistics depends on measurement of continuous and discrete variables.
BIOSTATISTICS: Is the application of statistical techniques to scientific research in
health related fields, including medicine, biology and public health and the
development of new tools to study these areas.
Biostatistics use statistical techniques to:
Design experiments to collect the right data.
Collect and analyze data from experiments.
Interpret the results of experiments.
Account for biases, variables and missing data.

FREQUENCY DISTRIBUTION:
• A frequency distribution shows the repeated items in a graphical form. it gives display
of the frequency of items or shows the number of times they occurred.
➤ Frequency distribution is used to organize the collected data in table form. The data
could be as marks scored by students, temperature of different towns, points scored in
volleyball match etc..,
➤ After data collection we have to show data in a meaningful manner for better
understanding organize the data in such a way that all it's features are summarized in a
table this is known as frequency distribution.
Ex-1: scores of 10 students in the G.K quiz are 15,17,20,15,20,17,17,14,14,20. let's
represent this data in frequency distribution.

APPLICATIONS OF STATISTICS IN PHARMACY:
1. Analytical Statistics such as Correlation, Regression is used to establish the functional
relation between variables like Concentration versus Absorbance, Time versus Amount of
drug dissolved.
2. Discriptive statistical parameters such as Mean and Standard deviation are used to
express the data generated from the replicated experiments to confirm reproducibility.
3. Inferential statistical tests such as T-test, ANOVA are used in bioavailability and
bioequivalence studies.
4. Applied statistics is used in quality control.
5. Statistical treatment of data is required for validation of a process.
6. Statistical quality control charts are used to determine the quality of product.
7. Statistical knowledge is essential for validation of analytical technique.
8. A useful tool in the design of experiments like bioavailability studies.
9. Useful in interpretation of experimental results.
10. Statistical usage is recommended by the drug regulatory agencies.
11. Collection of true representative sample from the bulk needs the concept of statistics

• Most of the cases population mean advisable to measure is not due to
problems in identifying all population suffering with disease more time
requirement, highly expensive, ethical and impracticable.
• So Sample of 'n' objects is taken from a Population to estimate the properties
of population
• Merits of Arthematic Mean :-
Easy to understand and calculate.
It takes all values into consideration. I
t is less affected by fluctuations of sampling.
Different interpretations by different persons are not possible.
• Demerits of Arthematic Mean :-
It cannot be determined by inspection nor by graphically.
It is very much affected by extreme values (1,2,3,4,5,75,95) mean value
doesnot furnish any information.

• Mode (Z):
• The mode is the value that occurs most frequently in the dataset. Unlike the mean
and median, The mode can be applied to both numerical and categorical data. It's
useful for identifying the most common value in a dataset.
• According to Croxton and Cowden "The mode of a distribution is the value at the
Point around which the items tend to be most heavily Concentrated"
• The plasma Concentration values observed from iv injection is 14,13,16,12,17, 16,
14, 12, 18, 14, 16,14.
• The mode is "14". The plasma conc observed after oral administration is
4,6,2,8,10,6,4,6,8,10,6,8. The mode is "6".
• Advantages of Mode:
➤ It is readily understood and easily calculated.
➤ It is not affected by Extreme observations.
• Disadvantages of Mode:
➤ It is not based on all observations
➤ It is not Capable of further mathematical treatment. It is affected by sampling

Median :-
• Median is the value of middle item of series arranged magnitudes in an ascending or
desending order of magnitudes
• The Median is the center point of distribution it divides data into two equal parts.
It is calculated with the following steps:
1. Collect the data.
2. Arrange the data in rank order.
3. Observe the central value in case of odd number of observations.
4. The mean of two central values in case of even observations and express it is the
median value.
Ex-1: Calculate the median plasma concentration of different patients by oral route
5,6,7,8,7,5,7,6 and 7.
Arranged in ascending order 5,5,6,6,7,7,7 and 8 Central value median is "7"
Ex-2: If number of observations in a series is even take the average of two middle values
as median. Calculate median for the data 2,4,5,6, 2,4,5,7,5 and 2
Arranged in ascending order 2,2,2,4,4,5,5,5,6 and 7 Central values are the average of 4,5
and the median is 4+5/2 = "4.5"

Percentile x100
• Ex: 12,000 students appeared for GPAT Examination 11.900 students got less
than marks than sri hari then the percentile score of Sri hari is
11900/12000=0.9916; usually it is mulltiplied with 100 then the values becomes
99.16.
• percentileX100 = 99.16
• Advantages of Median:
➤ It is easy to calculate and is readily understood. It is not at all affected by
extreme values.
➤ The median value can be located graphically.
➤ It is only average that can be used in qualitative analysis.
Disadvantages of Median:
➤ It cannot be exactly determined in case of even no.of observations.
➤ It is much affected by Fluctuations of Sampling.

Measures of Central dispersion :
• Disperson is useful to know variability in the data.
• It finds how individual value are spread around the Central value or mean value or
Average value.
• Brooks and Dick define "dispersion is the degree of the scatter or variation of the
variable about central value.
Objectives:
• To judge the reliability of measures of central tendency.
• To Compare different sets of data with respect to variability.
• To control the variability in data.
Methods of measuring dispersion 1. Range
2. Mean deviation
3. Variance and standard deviation.
I.Range :-
• It is a simple method to study the dispersion Range = Heighest value - Lowest value.

Ex: Range of 5,10,18,19,23,27.
Range =Heighest value - Lowest value.
27-5 = 22
Coefficient of Range
= 0.6875
Merits of Range:
➤ Easy to calculate
Demerits of Range:
Not based on all observations.
Much affected by fluctuations of sampling.
Not suitable for mathematical treatment.

2. Mean deviation (or) Average deviation :-
• Mean deviation is a measure of dispersion based on all observations.
• The Mean deviation is the arthimatic mean of the deviation of the
individual values from the average of given data.
• Mean deviation Can be computed from any average i.e.., Mean, Median
and Mode, but Mean is preferable because it is a more appropriate
measure of central value.
• Mean deviation
• Where,
∑i=Summation
x = Individual values
= Mean
|| = Modulus (-ves into +ves)

Ex: Absorbance values from spectrophotometer are
0.104,0.108,0.112,0.117,0.106, and 0.114 calculate mean
deviation.
0.1101 n=6
Mean deviation
Mean deviation= 0.00416

Coefficient of mean deviation:
• Coefficient of relative Mean deviation will give a relative measure of
dispersion, Suitable to compare two or more series.
• Coefficient of mean deviation
• Ex: Absorbance of same solution by two different
spectrophotometers are 0.104,0.108,0.112,0.117,0.106 and 0.114.
• Coefficient of mean deviation = 0.0372

• Advantages of Mean Deviation
• It is easy to calculate when compare with other methods of
dispersion.
• Calculation involves all observations.
• It is less affected by Extreme values when Compared with
Standard Deviation.
• Disadvantages of Mean Deviation:
• It ignores -ve signs of deviation.

3. Standard deviation:
• It is the most appropriate method of dispersion
• It is first introduced by karl pearson in 1993.
• It is defined as the positive square root of the arthimatic mean of squares
of the deviations of given observations from their arthimatic mean.
Standard deviation (s) = √ = n-1 (n≤30) For sample(s)
Standard deviation (σ) = n(n>30) For population(σ)
• It is difficult to calculate population standard deviation.
• Standard deviation tells you how much data points vary from the average.
• High standard deviation means greater variation between the data points
of dispersion (Scattered).
• Low standard deviation all the values close together.

Variance:
• It is the square of Standard deviation. It shows how much data points
deviates from the mean. It is also known as mean Square deviation.
• It is Important measure in the quantitative analysis of data, In
biological, agricultural and medical sciences.
• Comparing two data sets with similar averages but one has higher
variants indicating more fluctuations.
Standard Variance () = (n≤30) For sample
Standard Variance () = (n > 30) For population

Advantages of Variance :
• All the data points are involved in calculation.
• Least effected by Sampling fluctuations.
• Useful to know reliability of means of two or more different series.
Disadvantages of Variance:
• Difficult to calculate.
• Affected by extreme values.

Coefficient of variation / Relative standard deviation (RSD):
• It is clear that standard deviation of height of plants cannot
compare with the standard deviation of weight of plants because
they are exprested in different units. i.e.., Height in (cm) and weight
in (gm).
• So the meature Standard deviation must be converted into a relative
measure for the purpose of Comparision.
% Relative Standard Deviation (or) C.V = 100
Where,
S = Sample Standard deviation.
= sample mean.
• RSD always expressed in terms of %.
• RSD should be < 2%

• Ex:1- Calculate the mean, mean deviation, Standard deviation, %RSD for the
peak areas of Chromatograph 14400, 14980, 15046, 13975, 14295, 15200.
Mean=14,619
Mean deviation = 426
Standard deviation = 492.41
%RSD 3.36
• Ex:2 - Calculate mean, mean deviation, standard deviation, %RSD plasma
concentrations of 2.4,2.8,3.1,2.7,2.2,2.9.
Mean 2.683
Standard deviation = 0.3435
Mean deviation = 0.283
%RSD 12.802

Correlation:
• It measures the closeness of the relationship between two variables
(independent and dependent variables)
• The word relationship indicates that there is some Connection to
measure the closeness of the relationship between the variables.
• Ex: 1. concentration (independent variable) vs absorbance
(dependent variable)
2.dose of drug (independent variable) vs response (dependent
variable)
3. Time (independent variable) vs drug disolved (dependent variable)
• Mathematical formula established by - Karl pearson
• Graphically represented by Sir francis galton
• Corelation analysis helps to determining the degree of relationship
between two or more variables but it doesnot indicate a cause and
effect of relationship between two variables.

Types of correlation :
• Based on nature of relationship
1. positive (or) negative Correlation
2. Linear (or) non-linear correlation
3. Simple (or) multiple correlation
4. partial (or) total correlation
1.Positive Correlation :
Increase in the value of one variable is associated with an increase in the
value of other variable or decrease in the value of one variable is associated
with an decrease in the value of other variable

• Negative Correlation : As the one variable increases second
variable decreases and vice versa.
2. Linear Correlation :
If the variation in the values of two variables has a constant ratio.
Ex:- Variables (x) = 10 20 30 40 50
Variables(y)= 20 40 60 80 100

• Non-linear correlation : If the variation in the values of two variables
doesnot show constant variation.
• Simple correlation:
• It involves two variables or can include relationship between two variables.
Ex:- Amount of drug dissolved and hardness
• Multiple correlation: It involves a dependent variable and two or more
independent variables.
• Ex:- Relationship between amount of drug release (dependent variable) and
Hardness, granule size (independent variable)
• Partial correlation : In the study of relationship between two variables,
excluding some other variables.
Ex:- Potency of the drug is influenced by humidity and temperature .but
potency of drug effect of temperature is only studied, neglect the effect of
humidity.

• Total correlation : It involves study of effect of all independent variables or
dependent variables.
• Ex: Relationship between potency of drug is dependent variable temp &
humidity.
Methods of studying correlation :
1. scatter or dot diagram method.
2. Graphical method
3. karl pearsons coefficient of correlation method.
1. Scatter or dot diagram method :- The diagram of dots or points Obtained is
called a scattered diagram or dot diagram with the help of this diagram we get an
idea about the relationship between two variables x and y.
a) strong positive correlation : As the value of 1 increases, y also increases
proportionately.
b) strong negative correlation : As the value of x increases, y increases
proportionately.

c) Weak positive Correlation :
As the value of x increases, y Increases but not proportionately.
d) Weak Negative Correlation :
As the value of x increases, y decreases but not proportionately.
e) Complex correlation :
y seems to be related to x, but complex.
f) No correlation:
No relationship between x and y.

2.Graphical method:
• Using graph paper can establish relationship between x and y Variables.
• X increases, Y also increases then it is said to be positive correlation.
• If X and Y it is ve move in opposite direction then Correlation.
• This type of graphical method is used in environmental biology and
general studies.
3. Correlation coefficient:
The above two methods are usedul to establish qualitative relationship only
without giving quantitative relation blw two vanables, the data is not valid

• Positive, negative correlation, the correlation coefficient value should be more than
0.99 in process validation of pharmaceutical industry. The rough guide for correlation
is follows:
<0.2 Slight or almost negligible relationship
0.2-0.4 Low correlation
0.4-0.7 Moderate correlation
0.7-0.9 High correlation
0.9 Very high correlation
 Based on 'r' values we can define relationship between two variables to give more
justification about the relation correlation coefficient subjected to "t- Test"
Where,
r = correlation coefficient
n = number of observations
n-2 degrees of freedom

• Now 't' calculated value compare with 't' table value.
• To record the 't' table value, fix probability either 0.05 (5% bias, 95%
confidence) or 0.01 (1% bias, 99% confidence)
• If calculated t value is > table t value indicates Real correlation.
• If calculated t value is < table y value indicates No correlation.

INTRODUCTION OF STATISTICS FINAL YEAR VIII SEM

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