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Assignment # 2 (Lessons 10-15)

Question 1:                                                                                                                        (Marks: 3+5=8)

a)      The fourth mean moment of a symmetric distribution is 243. What would be the value of the standard deviation in order that the distribution may be meso-kurtic?

b)      Two candidates X and Y at the B.A (Hons.) Examination obtained the following data.

 Candidate X Candidate Y = 43.2 = 20.5 S.D = 24.25 S.D = 15.6

Which of the candidate showed a more consistent performance?

Question 2:                                                                                                             (Marks: 2+5=7)

1. If coefficient of skewness = 0, then what would you say about the shape of the distribution?
2. The following data were computed from personnel records of a manufacturing firm:

X = Number of years of service

Y = weekly wage rate

n = 23; ∑X = 2433; ∑Y = 4254, ∑  = 281019;  = 841786 and = 482788

If the correlation coefficient indicates that there does exist a relationship between X and Y,                                    compute the least squares line of regression Y = a + b X.

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question no 01  part   a

How To Calculate Standard Deviation

First, you need to determine the mean. The mean of a list of numbers is the sum of those numbers divided by the quantity of items in the list (read: add all the numbers up and divide by how many there are).

Then, subtract the mean from every number to get the list of deviations. Create a list of these numbers. It's OK to get negative numbers here. Next, square the resulting list of numbers (read: multiply them with themselves).

Add up all of the resulting squares to get their total sum. Divide your result by one less than the number of items in the list.

To get the standard deviation, just take the square root of the resulting number

I know this sounds confusing, but just check out this example:

your list of numbers: 1, 3, 4, 6, 9, 19

mean: (1+3+4+6+9+19) / 6 = 42 / 6 = 7

list of deviations: -6, -4, -3, -1, 2, 12

squares of deviations: 36, 16, 9, 1, 4, 144

sum of deviations: 36+16+9+1+4+144 = 210

divided by one less than the number of items in the list: 210 / 5 = 42

square root of this number: square root (42) = about 6.48

# What Is a Mesokurtic Curve?

Suppose you were graphing the performance of a large number of students on a standardized test. Most students will fall close to the middle. Only a few will do significantly better or worse than average. The number who do exceptionally better or worse will be smaller still. The result is a curve that starts off with a low value, indicating the small number who did very poorly, rises to a peak to indicate the majority of students with an average performance, then slopes off again to show the relatively small number who do above average, declining further to reflect the even smaller number who did exceedingly well. Statisticians describe such a curve as platykurtic, leptokurtic or mesokurtic depending on its shape.

A.O.A.

Sir plz esy explain kar dain

How square root of this number: square root (42) = about 6.48 ???

wrong question hn ye

Question no 02  part a

If coefficient of skewness is zero then distribution is symmetric or zero skewed.

question no 2 part  b

## The least squares regression line

The least squares regression line is the line which produces the smallest value of the sum of the squares of the residuals. A residual is the vertical distance from a point on a scatter diagram to the line of best fit. Therefore the least squares regression line can be seen as the best line of best fit.

The equation of the least squares regression line of y on x is:

Where b is:

As you can see there are 3 different ways to calculate the value for b, based on what information you are given in the question

#### Example

Calculate the least squared regression line of y on x from the following data:

 x 20 30 40 50 60 70 y 2.49 2.41 2.38 2.14 1.97 2.03

Firstly draw up a table of the values you need and fill it out. In this example we'll use the third equation for b so we need all the values of x2 and xiyi:

 x y x2 xiyi 20 2.49 400 49.9 30 2.41 900 72.3 40 2.38 1600 95.2 50 2.14 2500 107 60 1.97 3600 118.2 70 2.03 4900 142.1 Sum: 270 13.42 13900 584.7

Next step is to calculate the means of the x and y values:

Now the value of b can be calculated:

Hence the equation is therefore:

Cleaning it up:

mjy 1st question k 1st part ki samj ni aie tariq bro or last question me ye formula b luga skty hen sum y* sum x2-sum *sumxy divided by b somrethng he is se b nikal skty hen

STA301_Assignment#02-Solution_Fall_2012_(www.vustudents.ning.com)

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thnx again Thank u

ye solution tek ha download kr la aur khd sy edit kr lay

bye

QUESTION # 1 k fst part ki smjh ni aa rhi

simple hai

S.D mtlb Standard deviation = second moment

if dstrubtion is mesokutric then b2( 2 small hai). = 3

given hai moment 4 = m4= 243

b3 = m4/ m2 ka squr = 3

aur ab simple hai (m small 2 ka square) solve kar lo

243/ m2 ka square = 3

now

m2 ka squre= 243/3= 81

ab under root lay lo 9

m small ka square 2 ksy solve krna

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