STANDARD DEVIATION.pptx

It was first used by Karl Pearson in the year 1893. It can be defined as the square root of the arithmetic average of the square of the deviations measured by the mean.
It is also referred as Root Mean Square Deviation. It is denoted by Greek Letter word σ. It is always calculated by mean. Signs are not ignored in Standard Deviations

1. GOVERNMENT PHARMACY COLLEGE SAJONG Presented By, Abhilash Poudyal 18GPC002 Class PRESENTATION on STANDARD DEVIATION BIOSTATISTICS AND RESEARCH METHODOLOGY , BACHELOR OF PHARMACY

2. STANDARD DEVIATION It was first used by Karl Pearson in the year 1893 It can be defined as the square root of the arithmetic average of the square of the deviations measured by the mean. It is also referred as Root Mean Square Deviation . It is denoted by Greek Letter word σ . It is always calculated by mean. Signs are not ignored in Standard Deviations.

3. Methods of Calculations for SD INDIVIDUAL SERIES Actual mean method Direct method Short cut method or Assumed mean method Step deviation method 2) DISCRETE SERIES Actual mean method Direct method Short cut method or Assumed mean method Step deviation method 3) CONTINOUS SERIES Actual mean method Direct method Short cut method or Assumed mean method Step deviation method

4. INDIVIDUAL SERIES A) Actual mean method In this method, deviations are taken from actual mean. STEPS Calculate the actual mean (x̅) of the observation using formula= Σ X/N Find out the deviation of each item of the series from using ( X- X̅) and denote the deviation by x. Square the deviations and obtain the total = Σ x 2 Apply formula σ = √ Σ x 2 /N

5. B) Direct Method In this method standard deviation is calculated without finding deviations from actual mean STEPS Calculate actual mean (X̅) of the observation using formula= Σ X/N Square the observations and obtain the total = Σ x 2 Apply formula σ = √ Σ x 2 /N –(X̅) 2

6. C ) Short cut method or Assumed mean method STEPS Take any value of X in the series and assume it as Assumed mean( A ). Find out deviation from (A) and denote it as d= X-A . Calculate the sum of deviation to obtain Σ d Square the sum deviation to obtain Σ d 2 Substitute the value of Σ d and Σ d 2 in the formula √ Σ d 2 /N – √( Σ d/N) 2

7. D) Step deviation method STEPS Take any value in the series as assumed mean (A) Deviations are taken from the assumed average as d= X-A The deviations are divided by common factor as d’= d/c Sum of step deviations are obtained, also step deviations are squared and sum total is obtained. Formula, √ Σ d’ 2 /N – √( Σ d’/N) 2 X C

8. 2) DISCRETE SERIES Actual mean method Calculate the actual mean X̅ of the series as X̅ = Σ fX/ Σ f Find out deviation of items from actual mean by X-X̅. Square the deviation and multiply them with their respective frequencies (f) and obtain the total = Σ fX 2 Apply formula= √ Σ fx 2 /N

9. B) Direct Method Calculate the actual mean X ̅ of the series as X̅ = Σ fX/ Σ f Square the observation to get X̅ 2 Multiply frequency (f) to X 2 and obtain total = Σ fx 2 Apply the formula √ Σ fx 2 /N –(X̅ ) 2

10. C) Short cut method or Assumed mean method Take any value of X in the series and assume it as Assumed mean( A ). Find out deviation from (A) and denote it as d= X-A . Multiply these deviations by the respective frequencies and obtain total = Σ fd Obtain the square of deviation = d 2 Multiply the squared deviation by respective frequencies and get total = Σ fd 2 Apply formula = √ Σ fd 2 /N – √( Σ fd /N) 2

11. D) Step deviation method STEPS Take any value in the series as assumed mean (A ) Deviations are taken from the assumed average as d= X-A The deviations are divided by common factor as d’= d/c to obtain step deviation Multiply the step deviation by the respective frequencies and obtain total = Σ fd ’ Calculate the square of step deviation = d’ 2 Multiply these squared step deviations by the respective frequencies and obtain total = Σ fd’ 2 Apply formula √ Σ fd’ 2 /N – √( Σ fd ’/N) 2 X C

12. 3) CONTINOUS SERIES Actual mean method Calculate the actual mean X̅ of the series as X̅ = Σ fm / Σ f Find out deviation of mid point(m) from actual mean and calculate by m-X̅ and denote it by x Square the deviation and multiply them with their respective frequencies (f) and obtain the total = Σ fX 2 Apply formula= √ Σ fx 2 /N

13. B) Direct Method Calculate the actual mean X̅ of the series as X̅ = Σ fm / Σ f Square the observation to get m 2 Multiply frequency (f) to m 2 and obtain total = Σ fm 2 Apply the formula √ Σ fm 2 /N – ( X̅) 2

14. Take any value of mid point in the series and assume it as Assumed mean( A ). Find out deviation from mid point from assumed mean (A) and denote it as d i.e d= X-A . Multiply these deviations by the respective frequencies and obtain total = Σ fd Obtain the square of deviation = d 2 Multiply the squared deviation by respective frequencies and get total = Σ fd 2 Apply formula = √ Σ fd 2 /N – √( Σ fd /N) 2 C) Short cut method or Assumed mean method

15. Take any value of mid point in the series as assumed mean (A) Find out deviations of mid point from assumed mean as d= m-A The deviations are divided by common factor as d’= d/c to obtain step deviation Multiply the step deviation by the respective frequencies and obtain total = Σ fd ’ Calculate the square of step deviation = d’ 2 Multiply these squared step deviations by the respective frequencies and obtain total = √ Σ fd’ 2 /N Apply formula √ Σ fd’ 2 /N – ( Σ fd ’/N) 2 X C D) Step deviation method