The standard deviation is the square root of variance Standard deviation Direct method- SD is obtained from Assumed Mean (A) instead of Actual Mean ( ഥX)
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19 mai 2020 · Mean deviation Co-efficient of Mean deviation 4 Standard deviation Co- efficient of The formula is: Where, d-stands for the deviation from assumed mean = (X-A) http://www ddegjust ac in/studymaterial/mcom/mc-106 pdf
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The standard deviation is the square root of variance Standard deviation Direct method- SD is obtained from Assumed Mean (A) instead of Actual Mean ( ഥX)
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consider the range, Quartile Deviation, standard deviation etc In the latter are taken from the Assumed mean (A) and standard deviation is estimated by using
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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:Biostatistics
Measures of Dispersion-
Standard Deviation
Dr Madhu Rani (BOTANY) e-mail -madhupriya1999@gmail.comContact/Whatsapp-9412209655
theirunitofmeasureisalsosquared. squaredKg)Thestandarddeviationisthesquarerootof
variance Dr Madhu Rani (BOTANY) e-mail -madhupriya1999@gmail.comContact/Whatsapp-9412209655
ofmeasureisalsosquared.Standard deviation = variance
Variance = standard deviation2
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Definition
ofStandard
deviation (SDIt is also called root mean square deviation.
It is represented by Greek symbol ıand in short form by SD. It represents the extent to which individual values differ from the average or Mean.Itisbasedonallobservations.
Dr Madhu Rani (BOTANY) e-mail -madhupriya1999@gmail.comContact/Whatsapp-9412209655
itemsfromthearithmeticmeanofthe.Calculation of Standard deviation
Formula
Where2 = population variance,
X = a variable,
ഥor Ɋ= population mean, andN = t0tal number of variables.
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Merits
of SD It summarizes the deviation of a large distribution from Mean in one figure. It is most reliable and dependable Measure of Dispersion.It helps in calculating the Standard Error.
It helps in finding the suitable size of sample for valid conclusions.It is less affected by fluctuations in sampling.
SD is rigidly defined, and its values are always definite.Demerits
of SD It gives more weightage to extreme value and left to the values that are closer to mean. The process of acquiring deviations and then taking square root involves lengthy calculations. Hence its calculation is not easy. Dr Madhu Rani (BOTANY) e-mail -madhupriya1999@gmail.comContact/Whatsapp-9412209655
Significance
of SDIt isthemostwidelyused measure of dispersion.
It is based on all the observations.
incomputingtheMeanDeviation. fluctuationsofsampling. spreadinthevicinityofMean. Dr Madhu Rani (BOTANY) e-mail -madhupriya1999@gmail.comContact/Whatsapp-9412209655
Step 1-arithmetic mean is calculated using the formula...Calculation
of SD Step 2-Deviationor difference of each observation from the Mean is calculated using the formula.... Step 3-This difference between observation and Mean is squared... step 4-All the squared values are added to calculate the sum of squared deviations, i.e., or Step 5-Calculate the variance (ı2) by using the where N -1is the number of observations minus one. Step 6-Find the square root of the variance to get Standard Deviation. i.e.,µ or
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Calculation
ofSD from
ungrouped data1. Indirect method.
1.Indirect method-SDisobtained from Mean using the following formula:
2. Direct method.
When N < 30
Wheredxor x= deviation obtained from actual Mean, i.e.,N=totalnumberofobservations
replacingഥwithA. Dr Madhu Rani (BOTANY) e-mail -madhupriya1999@gmail.comContact/Whatsapp-9412209655
Calculation
ofSD from grouped
data For grouped data, SD iscalculated either using Arithmetic Mean (Long method) or Assumed Mean (Short method) using the following formula: f = mid-point of each class orLong method
Short method
WhereݔԢ=
c = correction݅=Class interval
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Coefficient of Standard Deviation
formulaisused. Dr Madhu Rani (BOTANY) e-mail -madhupriya1999@gmail.comContact/Whatsapp-9412209655
deviation,roundedtotwodecimalplaces.Practiceproblem
Dr Madhu Rani (BOTANY) e-mail -madhupriya1999@gmail.comContact/Whatsapp-9412209655
10119.510111011.51110.511.5
91010.511.5119.510.5111110.5
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Solution
The sample variance, ɐ2, is equal to the sum of the last column (9.7375) divided by the total number of data values minus one, which is 19. భవ= 0.5125The sample standard deviation ߪ
variance:Rounded to two decimal places, ߪ
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240.12240.13240.15240.12240.17
240.15240.17240.16240.22240.21
Example -3. Calculate the Mean and Standard Deviation from the following data. Leaf length (cm)90-9980-8970-7960-6950-5940-4930-39Frequency21222201421
Submit the
answers inth April 2020
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