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Numerical solution of a system of linear equations by
1) LU FACTORIZATION METHOD.
2) GAUSS ELIMINATION METHOD.
3) MATRIX INVERSION BY GAUSS ELIMINATION METHOD.
Numerical solution of a system of linear equations by
1) LU FACTORIZATION METHOD.
2) GAUSS ELIMINATION METHOD.
3) MATRIX INVERSION BY GAUSS ELIMINATION METHOD.
Estimation Theory Class (Summary and Revision)Ahmad Gomaa
Summary of important theories and formulas in Estimation theory:
1) Cramer-Rao lower bound (CRLB)
2) Linear Model
3) Best Linear Unbiased Estimate (BLUE)
4) Maximum Likelihood Estimation (MLE)
5) Least Squares Estimation (LSE)
6) Bayesian Estimation and MMSE estimation
Here we have included details about relaxation method and some examples .
Contribution - Parinda Rajapakha, Hashan Wanniarachchi, Sameera Horawalawithana, Thilina Gamalath, Samudra Herath and Pavithri Fernando.
Estimation Theory Class (Summary and Revision)Ahmad Gomaa
Summary of important theories and formulas in Estimation theory:
1) Cramer-Rao lower bound (CRLB)
2) Linear Model
3) Best Linear Unbiased Estimate (BLUE)
4) Maximum Likelihood Estimation (MLE)
5) Least Squares Estimation (LSE)
6) Bayesian Estimation and MMSE estimation
Here we have included details about relaxation method and some examples .
Contribution - Parinda Rajapakha, Hashan Wanniarachchi, Sameera Horawalawithana, Thilina Gamalath, Samudra Herath and Pavithri Fernando.
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3. Rentang semikuartil
4. Rentang a-b persentil
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6. Variansi
7. Ukuran penyebaaran relatif
8. Bilangan baku
Identify the independent and dependent variable;
Draw the best fit line on a scatter plot;
Calculate the slope and the y-intercept of the regression line;
Interpret the calculated slope and the y-intercept of the regression line;
Predict the value of the dependent variable given the value of the independent variable; and
Solve problems involving regression analysis.
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2. STATISTICS INFORMATION
We can define statistics is a science in which we collect the data,
arrange it and by the analysis and interpretation of this the
organization make the decision.
. And data is the important tool of any organization.
. Data are divided in two parts 1. Quantitative data
2. Qualitative data
- by the uses of various mathematical function and various other tool
in excel we can analyze the data and we can find something valuable
in large data
3. STEM AND LEAF
-Stem-and-leaf plots are a method for showing the frequency with which certain classes of values
occur.
-You could make a frequency distribution table or a histogram for the values, or you can use a stem-
and-leaf plot and let the numbers themselves to show pretty much the same information.we can make
stem leam using manual calculation or either using REPT formula in excel.
DATA:
4
5
7 (a).Normal stem and leaf: (b).Stem and Leaf using REPT formula
8
16 Stem Leaf Stem Leaf
19 04578 04578
19 1699 1699
20 234599 20034599
20 30 30000
23 40 40
24 56 56
25
29
29
30
30
30
30
40
56
5. FREQUENCY DISTRIBUTION
-A frequency distribution provides a visual representation for the distribution of
observations within a particular test. Analysts often use frequency distribution to
visualize or illustrate tlhe data collected in a sample.
- we have taken some data lets consider it is the price of 15 bike(rupees) given in
table.
price of bike in
rupees
641773555345546
324553432144224
345233333293753
353535323433664
352233544644456
6. DETERMINATION OF CLASS AND
WIDTH
-to determine the number of classes (k) is the “2 to the k rule.”
such that 2k > n.
Here we have n=15 so 2^4=16
-for the determination of the width we have the formula
i (H-L)/k where i is the class interval, H is the highest observed
value, L is the lowest observed value, and k is the number of
classes.
So the interval we got 15324.5 round
Up the value to 15325
price of
bike in
rupees
64177 35553 45546
32455 34321 44224 max 93753
34523 33332 93753 min 32455
35353 53234 33664
interva 15324.
7. CLASS REPRESENTATION
I HAVE USED THIS DATA FOR FOLLOWING SLIDE GRAPH
PREPRATION
class of the price frequency cumulative frequency relative frequency
32000-47325 11 11 0.733333333
47325-62650 2 13 0.133333333
62650-77975 1 14 0.066666667
77975-93300 1 15 0.066666667
total=15
8. HISTOGRAM OF PRICE RANGE VS FREQUENCY
0
5
10
15
20
25
32000-47325 47325-62650 62650-77975
Chart Title
frequency cumulative frequency
11. PERCENTILE
A percentile is a measure at which that percentage of the total values are the same
as or below that measure. For example, 90% of the data values lie below the 90th
percentile, whereas 10% of the data values lie below the 10th percentile.
Formula:-(n+1)p/100 where p= percentile and n= total number
Eg. We have 6,9,23,25,35,36,57,74,calculate the 50th percentile
Solution here total no. n=8 p = 50 put these value in the formula
So we get (8+1)50/100 = 4.5 so the 50th percentile is 25.5
By the above way we can find any percentile
12. QUARTILE- Quartile are the percentage point that break down the data set into
quarter like 1quater 2nd quarter 3rd quarter, 4th quarter
1quartile= 25% percentile
2nd quartile= 50% percentile
3rd quartile= 75% percentile like wise
Formula= 1st quartile= ¼(n+1)th term
3nd quartile= 3/4(n+1)th term like wise.
Eg .2,3,5,6,8,9 find the 1st and 3rd quartile of this data
Solution
Here n= 6 so 3rd quartile ¾(6+1)th term= 5.25th term so it will be
8.25
1st quartile= ¼(6+1)th term= 1.75th term so it will be 2.75
13. QUATILE RANGE
Quartile range is the difference between 3rd-1st quartile
So we have 3rd quartile =8.25
And 1st quartile= 2.75 so inter quartile range will be
8.25-2.75=5.5
14. VARIANCE AND STANDARD DEVIATION
-The variance (symbolized by S2) and standard deviation (the square
root of the variance, symbolized by S) are the most commonly used
measures of spread.
Variance formulation it is for the population for
samle put in place of n (n-1) in dominator
- standard deviation is the square root of variance so the formula will
be
This for applied for the discrete types of data for the continuous data
other formula is utilize
15. FOR DISCRETE DATA
USING PREVIOUS SLIDE FORMULA IN EXCEL WE FIND OUT THE
VARIANCE AND S.D OF GIVEN DATA
item priceXmean(X bar) X-Xbar (X-Xbar)^2
43 42.33333333 0.666666667 0.444444444
34 42.33333333 -8.333333333 69.44444444
35 42.33333333 -7.333333333 53.77777778
23 42.33333333 -19.33333333 373.7777778 variance 197.5556
53 42.33333333 10.66666667 113.7777778 S.D 14.05545
45 42.33333333 2.666666667 7.111111111
24 42.33333333 -18.33333333 336.1111111
67 42.33333333 24.66666667 608.4444444
57 42.33333333 14.66666667 215.1111111
1778
total 381 here n=9
16. CONTINUOUS DATA
VARIANCE AND S.D CALCULATION
FORMULA FOR VARIANCE= sigma(X-Xbar)^2f/sigmaf
Where f= frequency x is the the given data value xbar is mean and
sigma means sum of all
- and the standard deviation as we know it will be square root of the
variance
18. MEAN, MEDIAN MODE
1, UNGROUPED DATA
Mean- it is the sum of all number divided by total number
Median- it means the middle value
Mode – it means the most repetitive number in data know as mode
Take eg. If 2,4,5,3,5,5,4,6,5 is the given data find mean, median
mode data
2 mean 4.333333
3 median 5
4 mode 5
4
5
5
5
5
19. MEAN, MEDIAN AND MODE OF
GROUPED DATA
Mean = sigma fx/sigma f
Where f is the frequency and x is the mid value of the grouped data
w(kg) frequency mid value(X) fX c frequency
54-57 5 55.5 277.5 5
58-61 7 59.5 416.5 12
62-65 10 63.5 635 22
66-69 12 67.5 810 34
70-73 6 71.5 429 40
74-77 5 75.5 377.5 45
78-81 4 79.5 318 49
82-82 1 83.5 83.5 50
50 3347
here we have
sigmafx 3347
sigmaf 50
mean 66.94
23. CALCULATION OF MODE
w(kg) frequency mid value(X) fX c frequency
54-57 5 55.5 277.5 5
58-61 7 59.5 416.5 12
62-65 10 63.5 635 22
66-69 12 67.5 810 34
70-73 6 71.5 429 40
74-77 5 75.5 377.5 45
78-81 4 79.5 318 49
82-82 1 83.5 83.5 50
50 3347
here given using slide formula in excel
L 66 mode 66.75
f1 12
f0 10
f2 6
i 3
24. COVARIANCE
Covariance is a statistical tool that is used to determine the relationship between the
movement of two asset prices.
25. CALCULATION
using formula given in slide
x Y x-xbar y-ybar (x-xbar)*(y-ybar)
22 21 -9.71429 -55 534.2857143 covariance -589.857
44 23 12.28571 -53 -651.1428571
-12 3 -43.7143 -73 3191.142857
23 54 -8.71429 -22 191.7142857
14 353 -17.7143 277 -4906.857143
67 43 35.28571 -33 -1164.428571
64 35 32.28571 -41 -1323.714286
-4129
average 31.71429 76
n 7
26. THE COEFFICIENT OF
CORRELATIONcorrelation coefficients are used to assess the strength and direction of the linear
relationships between pairs of variables
Where sx is the standard deviation of x variable and sy is the standard deviation of y
variable
27. CALCULATION ON EXCEL
using formula given in slide
x Y x-xbar y-ybar (x-xbar)*(y-ybar)
22 21 -9.71429 -55 534.2857143 covariance -589.857
44 23 12.28571 -53 -651.1428571
-12 3 -43.7143 -73 3191.142857 Coeffient of correlation -2561.46
23 54 -8.71429 -22 191.7142857
14 353 -17.7143 277 -4906.857143
67 43 35.28571 -33 -1164.428571
64 35 32.28571 -41 -1323.714286
-4129
average 31.71429 76
n 7
S.D 26.27717 114.109
28. COEFFICIENT OF VARIANCE
The coefficient of variation (CV) is the ratio of the standard deviation to
the mean.
29. CALCULATION USING FORMULA
using formula given in slide
x Y x-xbar y-ybar (x-xbar)*(y-ybar)
22 21 -9.71429 -55 534.2857143 covariance -589.857
44 23 12.28571 -53 -651.1428571
-12 3 -43.7143 -73 3191.142857 Coeffient of correlation -2561.46
23 54 -8.71429 -22 191.7142857
14 353 -17.7143 277 -4906.857143
67 43 35.28571 -33 -1164.428571
64 35 32.28571 -41 -1323.714286
-4129
average 31.71429 76
n 7
S.D 26.27717 114.109
coefficient of variance 82.85595 150.1434
30. IF FUNCTION
The IF function runs a logical test and returns one value for a TRUE result, and
another for a FALSE result.
BY using this if function in excel we can performed the logical test we can find
true, flase and several other parameters using ifs and if function
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31. VLOOKUP
VLOOKUP stands for 'Vertical Lookup'. It is a function that makes Excel search for
a certain value in a column (the so called 'table array'), in order to return a value
from a different column in the same row.
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32. HLOOKUP
HLOOKUP when your comparison values are located in a row across the top of a
table of data, and you want to look down a specified number of rows.
Product idProduct namecountry email
2002 Xylocaine Bolotnoyelnials0@accuweather.com
2004 LANEIGESkin Veil Foundation EX No. 23Sand BeigeNyazepetrovskdhadye1@biblegateway.com Product id product name country email
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2012 ZOCOR Warungbuahlbosward8@seattletimes.com
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33. VLOOKUP RANGE USING IF
FUNCTIONThe range of cells in which the VLOOKUP will search for the lookup_value and
the return value. You can use a named range or a table, and you can use names in
the argument instead of cell references.
Applied formula for calculation in excel is
IF(ISTEXT(F5),VLOOKUP(F5,B5:D8,3,0),VLOOKUP(F5,C5:D8,2,0))
If Formula with Vlookup
Name ID Rank Name Or Id Rank
Anil 1001 A 1001 A
Jack 1002 B
Rahul 1003 C
Aman 1004 D
34. DATA AND DATA BASE
Sumif:-The SUMIF function returns the sum of cells in a range that meet a single
condition. The first argument is the range to apply criteria to, the second argument is the
criteria, and the last argument is the range containing values to sum.
I utilize this formula in excel
SUMIF(M11:M18,"sun",O11:O18)
day product sale
sun detergent 122
mon milk 124 total Sunday sale
tue rice 245 3789
wed cheese 5335
thrus rice 355
fri t shirt 345
sat frok 355
sun meat 3667
35. SUMIFS
SUMIFS is a function to sum cells that meet multiple
criteria. SUMIFS can be used to sum values when adjacent cells meet
criteria based on dates, numbers, and text. SUMIFS supports logical
operators (>,<,<>,=) and wildcards (*,?) for partial matching.
Used formula in excel
SUMIFS(C2:C11,A2:A11,Npath,A2:A11,Oloo
EMPLOYEESCOLOUR SALE
Npath Purple $6.29
Skibox Puce $9.87
JabbersphereGoldenrod $8.73
Aimbu Aquamarine $5.01
Demivee Mauv $0.31 npath and oloo total sales
PhotobeanGoldenrod $6.35 $11.62
Dynazzy Teal $1.91
Blogspan Orange $4.55
Ailane Purple $9.88
Oloo Maroon $5.33
36. AVERAGEIF
The AVERAGEIF function in Excel calculates the average of cells that meet one
criteria. AVERAGEIFS calculates the average of cells that meet multiple
criteria.
Formula used in excel
=AVERAGEIF(B2:B11,"Purple",C2:C11)
EMPLOYEESCOLOUR SALE
Npath Purple $6.29
Skibox Puce $9.87
JabbersphereGoldenrod $8.73
Aimbu Aquamarine $5.01
Demivee Mauv $0.31 average of purple
PhotobeanGoldenrod $6.35 $8.09
Dynazzy Teal $1.91
Blogspan Orange $4.55
Ailane Purple $9.88
Oloo Maroon $5.33