TOPIC: RANGE, MEAN DEVIATION, QUARTILE DEVIATION
Sruthi. K. S
1st SEM MSc Zoology
Roll No: 111705
SL No:| Content| Page No:|
1234| IntroductionMeasures of dispersionConclusionReference| 34 – 171819|
Biostatistics is the application of statistical methods to the problems of biology, including human biology, medicine, public health, agriculture, veterinary and genetics. The primary aim of statistical methods is to condense the raw data in a way that it is able to convey some meaningful conclusion at the first sight. The single value expression or presentation of data is called central value. The values of variable tend to concentrate around the central value, which is also called central tendency. Whatever measure of central tendency is selected to represent the data, it fails to provide the complete picture for a set of data because they all are a single representative value of that data. For ascertaining the deviations from the central value there are certain specific measure of dispersion, or deviation. Measure of dispersion or variability is the number that conveys the relative position of an item or a data value in the data set. A number of measures we used to describe the variability in data. These are range, selected percentiles, quartile deviation, standard deviation, mean deviation and the coefficient of variation. The measure of variance or dispersion is an important tool in bio statistical studies because biological phenomena are more valuable than physical and chemical phenomena.
Measures of dispersion
Measure of dispersion is the number that conveys the relative position of an item. The deviations from the central value are obtained by certain specific measures of dispersion. The various methods used for measuring dispersion are divided into two categories. * Distance deviation measures: Distance measures use distance of spread between two values in the data set. The distance becomes a measure of variability or measure of dispersion. Range, percentiles and quartile deviation are methods for the study of measure of dispersion by distance * Average deviation measures: These are the average of deviation determined from the measure of central tendency. They are used more commonly for measuring variability or dispersion. Mean deviation, standard deviation, coefficient of variation and variance are such measures of dispersion.
Dispersion may be measured in terms of the difference between two values of a series. The range is the simplest method of studying dispersion. It is defined as the difference between the highest and the lowest values of the variable in a distribution. The range gives a comprehensive value for the data in that it includes the limits within which all the items occurred. Symbolically * Range of ungrouped data is given by the formula
Range (R) = Highest value (H) –Lowest value (L) of given data * Range of grouped data is given by the formula
H = Upper true limit of the highest class
L = Lower true limit of the lowest class
Coefficient of range
The coefficient of range is the relative measure of corresponding range. It is obtained
by applying the following formula
Coefficient of range = H-L/ H+L
H= highest value L = lowest value EXAMPLE NO: 1
Data on no: of secondary branches in a pulse are given below. Find out the range and its coefficient? No: of secondary branches = 8, 10, 15, 18, 17,26,22,20
The highest value is 26 while the lowest value is 8.
Range = H - L
=26 - 8
Coefficient of range = H-L/H+L = 26 – 8 / 26 + 8 =...