B. Sc (P) Life Science III year Semester VI
DSE-1: Analytical Techniques in Plant Sciences
Dr Madhu Rani
Department of Botany, DBC, DU
Unit 7:BiostatisticsMeasures of Dispersion- Range
1
Dr Madhu Rani (BOTANY) e-mail - [email protected] Contact/Whatsapp- 9412209655
Introduction• The measures of central tendency (mean, median and mode) are not adequate to describe data.
• Two data sets can have the same mean, but they can be entirely different.
• Thus to describe data, one needs to know the extent of variability.
• This is given by the measures of dispersion.
• In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is
stretched or squeezed.
• The following three sets of data are not identical, yet their mean values are same. However, their range
is different.
Series 1 60, 60, 60, 60, 60 Mean=60 Range= 60
Series 2 30, 50, 85, 75, 60 Mean=60 Range= 30 – 85
Series 3 10, 60, 90, 90, 50 Mean=60 Range= 10 – 90
• A measure of dispersion reflects how closely the data clusters around the measure of central tendency.
It represents the deviation of value of individual observations on either side of the central value in a set
of data. 2Dr Madhu Rani (BOTANY) e-mail - [email protected] Contact/Whatsapp- 9412209655
Importance of dispersion
The measure of variance of dispersion is an important tool in biostatistical studies because biological
phenomena are more valuable than physical and chemical phenomena.
For example- Individual variations are found in hemoglobin percentage,
in the number of RBCs and WBC, and even
the cure rate with the same drug where is in different patients of the same age and sex.
The major objective of measures of dispersion are-
❖ To judge the reliability of measure of Central tendency.
❖ To obtain correct picture of distribution or dispersion of values in the series.
❖ To make a comparative study of variability of two or more series or samples.
❖ To identify causes of variability in samples in order to exercise corrective measures as in the case of
body temperature, blood pressure and pulse rate, etc.
❖ To use dispersion values for further statistical analysis.
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Requisites of a good measure of dispersion
A good measure of dispersion should have the following properties:
▪ Measure of dispersion should be precisely and clearly defined.
▪ It should be easily understood as a measure of variability in the data.
▪ Measure of dispersion should be based on all observations of the data.
▪ It should not be unduly influenced by the extreme values.
▪ It should be easy to calculate.
▪ Measure of dispersion should be capable of being treated algebraically.
The two types of measures of dispersion are -
1. Absolute measures of dispersion
2. Relative measures of dispersion
Types of measures of dispersion
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5Dr Madhu Rani (BOTANY) e-mail - [email protected] Contact/Whatsapp- 9412209655
Absolute measures of dispersion are expressed in the same unit in which observations are given.
These measures are useful for comparing variation in two or more distributions where units of measurement are
the same.
These measures cannot be used for comparing the variability of distributions express in dissimilar units.
Absolute measures of the following types-
1. Distance deviation measures or measures of limits- these use distance of spread between two values in
the data set. This distance becomes a measure of variability on measure of dispersion. The larger the
distance between two values the greater is the variability.
The methods for the study of measure of dispersion by distance include range, percentiles, quartile
deviation, semi-interquartile deviations.
2. Average deviation measures- are the average of deviation determined from the measure of Central
tendency. They are used more commonly for measuring variability or dispersion.
These include mean deviation, standard deviation and variance.
Relative measures of dispersion - these are expressed as a ratio or percentage of all the coefficient of the
absolute measures of dispersion. Therefore, relative measures of dispersion are also called coefficient of
dispersion. These are pure unit unless numbers. Relative measures are used for comparing variability in two or
more distributions having different units of measurements.6Dr Madhu Rani (BOTANY) e-mail - [email protected] Contact/Whatsapp- 9412209655
• Range is the difference between the lowest and the highest values present in the observations in a
sample.
• Example- If there are 20 observations on seed oil content in Groundnut, the highest value being
65% and the lowest 25%. The range will be 65-25 = 40.
• Thus, it is a measure of the spread of variation in a sample.
• It is the simplest possible measure of variability and its computation is very easy.
Range = Maximum value — Minimum value.
Range:
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Range for epidemic period without measures
Range for epidemic period with measures
The course of an epidemic is shaped by a variable called the
reproductive rate, or R. It represents, in effect, the number of
further cases each new case will give rise to. If R is high, the
number of newly infected people climbs quickly to a peak before,
for want of new people to infect, starting to fall back again (see
chart 2). If R is low the curve rises and falls more slowly, never
reaching the same heights. With sars-cov-2 now spread around
the world, the aim of public-health policy, whether at the city,
national or global scale, is to flatten the curve, spreading the
infections out over time.
This has two benefits. First, it is easier for health-care systems to
deal with the disease if the people infected do not all turn up at
the same time. Better treatment means fewer deaths; more time
allows treatments to be improved. Second, the total number of
infections throughout the course of the epidemic can be lower.
To flatten the curve you must slow the spread. The virus appears
to be transmitted primarily through virus-filled droplets that
infected people cough or sneeze into the air. This means
transmission can be reduced through physical barriers, good
hygiene and reducing various forms of mingle—a strategy known
as “social distancing”. Such measures are already routinely used
to control the spread of the influenza virus, which spreads in a
similar way and is responsible for hundreds of thousands of
deaths a year.
https://www.economist.com/briefing/2020/02/29/covid-19-is-now-in-50-countries-and-things-will-get-worse
The Economist
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Merits of Range
❖ It is easy to calculate, and easy to understand.
❖ It is useful in frequency distributions where only two
extreme observations are considered.
❖ It is extensively used as a statistical quality control.
❖ Its units are the same as a unit of the variable being
measured.
❖ The range when given along with the mean gives useful
information particularly when the data has a normal
distribution.
To measure of variability in plant breeding populations.
In analyzing the variations in the quality control of
products, medicines, antibiotics, tonics, etc.
In estimating fluctuations of observations in
meteorological department- difference between max. and
min. temperatures and humidity help in weather forecast.
Demerits of Range
❑ Range is very crude measure of variability.
❑ It is not capable of further algebraic treatment
and cannot be defined rigidly.
❑ Range is not based on the entire set of data. It is
based on two extreme observations, which
themselves are subject to change. So range
cannot be regarded as a reliable measure of
variability.
❑ Range is greatly affected by fluctuation of
sampling. The larger the number of variables,
the larger is the range. Its values vary widely
from sample to sample.
❑ Range cannot be used for open – end classes.
❑ Range is very sensitive to the size of the sample.
(The more is the number of observations in the
data, the better will be the variability range).
❑ It does not indicate as to how the data behave in
between the highest and the lowest value.
Uses of Range
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Calculation of Range
Range (R) = Highest value (H) – Lowest value (L)
Example: Hb% per 100 cc blood of 15 individuals is as follows. Calculate the range.
14.7 11.5 13.8 12.5 14.1 11.7 14.8 14.3
13.1 12.9 14.5 14.2 11.8 14.9 14.0
Solution: step 1: Arrange the data in ascending order
11.5 11.7 11.8 12.5 12.9 13.1 13.8 14.0 14.1 14.2 14.3 14.5 14.7 14.8 14.9
Step 2: The Lowest value is- 11.5 and the highest value is- 14.9
Step 3: The Difference between Highest value (14.9) and Lowest value (11.5) gives the Range
R = H – L
R = 14.9 – 11.5 = 3.4
The Range is 3.4 per 00 cc10Dr Madhu Rani (BOTANY) e-mail - [email protected] Contact/Whatsapp- 9412209655
Sources:
• Jerrold H. Zar. Biostatical Analysis. 5th edition.
• V. B. Rastogi. Biostatistics. 3rd revised edition.
• M.M. Triola, M.F. Triola and J. Roy. Biostatistics: for the Biological and Health
Sciences.
Practice question
Calculate the Range from the data related to number of flowers per plant for 15 plants of a Vernonia sp.
16 23 5 12 17 21 11 28 10 7 13 19 14 19 22
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