1) The document discusses various statistical analysis techniques including data tabulation, graphical representation, standard deviation, ANOVA, and linear regression analysis. 2) Data tabulation involves arranging data in logical tables to reduce space, explanations, and help with comparisons. Graphical representation involves using charts like linear, bar, and pie charts to visually depict relationships. 3) Standard deviation and standard error are discussed as measures of dispersion in a data series and sampling distribution respectively. ANOVA and linear regression are analyzed as methods to understand relationships between variables and predict outcomes.

1. STATISTICAL ANALYSIS
NAME- SAHIL THOOL
CLASS-TE(CHEMICAL)
ROLL NO -68
SUBJECT- PLANT ENGG.

2. STATISTICAL ANALYSIS CATEGORIES
• 1. Data tabulation
• 2.graphical representation
• 3.standard deviation
• 4.standard error
• 5.ANOVA
• Linear regression analyssis

3. Data tabulation
• Defination- arranging mass data in logical manner in terms of rows and tables
• It essential for – reducing space
• --reduce explaination
• --reduce description
• ---help comparision
• Proper reperenstation-
• Table No: Title
Sr. No. Time in min Concentration in mg/lit
i
ii 2*
iii

4. Graphical represenation
• Always draw on MS Excel or openoffice.org
• Its categories as
• ---linear chart
• ---bar chart
• ---pie chart
• Linear chart - y vs x called linear chart
4.3
2.5
3.5
2.4
4.4
1.82 2
3
0
2
4
6
Category 1 Category 2 Category 3
Chart Title
Series 1 Series 2 Series 3

5. -Bar chart-----
Pie chart reperesentation-
0
1
2
3
4
5
Category 1 Category 2
Chart Title
Series 1 Series 2 Series 3
Sales
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

6. Standard deviation
• It can be defined as stanadard which measures
dispersion in series

7. Degree of freedom-
• It is number of independent observation which makes up statistics is
known as ddegrre of freedom
• Notation--- d.f
• Df= no of independent observation-no of parametrs estimated
•
• Σ( ( x(i) – x(mean)) / σ )2

8. STANDARD ERROR
Standard deviation of sampling distribution called standard error
sample variance formula

9. Analysis of Variance
• One way anova
• Step1- obtain mean of each sample
• Step2 – obtain mean of mean
• Step3- Calculate square of variance betw sample
• Step4-calculate Sswithin
• Step5- find SS for total variance
• Ss for total variance= Sswithin + SS between

10. • Step6 – to find mean square betweem the sample
• Msbetween = ( SS between/ k-1)
• step7- to find mean square within
• MS within= (SS within/n-k)
• where(n-k) stands for degree of freedm within sample
• k= no of sample

11. .
• We know degree of freedom here
• (n-1)=(k-1)+(n-k)
• Step8 – find f ratio
• F ratio basd on statistics and follows F distribution with (n-1)(n-k) ie
degree of freedom
• It summarise as

12. Short cut ANOVA method
• Step1-Take the total of the values of individual items in all the
samples i.e., work out
Σxij
• Step2- Work out the correction factor as under:
Correction factor= T 2 / n
• Step3- Find out the square of all the item values one by one and then
take its total. Subtract the correction factor from this total and the
result is the sum of squares for total variance. Symbolically, we can
write:
Total SS=ΣXij
2-(T2/n)

13. .Step4-Obtain the square of each sample total (Tj)2 and divide such
square value of each sample by the number of items in the
concerning sample and take the total of the result thus obtained.
Subtract the correction factor from this total and the result is the sum
of squares for variance between the samples. Symbolically, we can
write:
SS between=
Σ(Tj)2/nj-(T)2/n

14. .
• Step5- The
Step5- The sum of squares within the samples can be found out by
subtracting the result of (iv) step from the result of (iii) step stated above
and can be written as under:

15. Linear regression analysis
• Linear regression consists of finding the best-fitting straight line
through the points. The best-fitting line is called a regression line. The
black diagonal line in Figure 2 is the regression line and consists of the
predicted score on Y for each possible value of X. The vertical lines
from the points to the regression line represent the errors of
prediction. As you can see, the red point is very near the regression
line; its error of prediction is small. By contrast, the yellow point is
much higher than the regression line and therefore its error of
prediction is large.
•

16. A scatter plot of the example data. The black line consists of the predictions, the
points are the actual data, and the vertical lines between the points and the black
line represent errors of prediction. The formula for a regression line is
Y' = bX + a
relation with error is Y=a+bx+error
therefore error = y-a-bx