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Dear students, 

 

The Assignment no.3 has been uploaded and it is graded. You have to solve only section C of Assignment 3.

Instructions about solving assignment must be strictly followed and provide assignment solution on MS Word file.

No assignment will be accepted through email so submit it within due date.

Section C

Question 1:

 

60

80

90

96

120

150

200

360

480

520

1060

1200

1450

2500

7200

The annual incomes (in thousands of $) of fifteen families is as

 

Calculate the

  • Geometric mean
  • Harmonic mean
  • Quartile deviation

for the given data.

 

Question 2:

 

Find the correlation between candidates score in interview and written test for a random sample of 6 candidates, which is as                                                               

 

X

2

4

5

6

8

11

Y

18

12

10

8

7

5

 

Where X=Interview marks, Y=Marks of written test.


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Replies to This Discussion

Plz share section D pllllzzzzzz

mth302 assignment solution

Attachments:

 

 

Section A:

 

Question No 1:

 

                 Arrange the following set of data in ascending order and write down the frequency table showing the frequency of each term in front of it

Solution:

 

1,1,1,2,2,2,2,3,3,3,3,3,3,5,5,5,5,5,6,7,7,7,8,8,8,8,9,9,9,10

 

 

 

Item

Frequency

Percentage

1

3

10.00%

2

4

13.33%

3

6

20.00%

5

5

16.67%

6

1

3.33%

7

3

10.00%

8

4

13.33%

9

3

10.00%

10

1

3.33%

Grand Total

30

100.00%

 

 

 

Part 2:               Find first second and third quartile of the following data

                 12, 18, 13,19,16,14,15,17,20.

Solution: 

This is ungrouped data. First arrange the data in ascending order.

12,13,14,15,16,17,18,19,20

Now, find median or second quartile. 16

Median position: (n+1) /2 = (9+1)/2=10/2=5th position Counting median= 16

 

First quartile (Q1) First Quartile Position: (n+1)/4 =10/4=2.5th position So average of 2nd and 3rd positions values= (13+14)/2=13.5

Third quartile (Q3) Third Quartile Position: 3(n+1)/4 =30/4=7.5th position So average of 7th and 8th position values= (18+19)/2=18.5.

 

 

 

Question No 2:

 

 

Find the correlation coefficient r between variables X and Y using the following table (Do not use excel formulas to find correlation coefficient)

 

 

 

x

4

3

5

7

y

7

8

9

12

 

 

Solution:

 

 

Now from the given data

 

 

      

Hence the describe estimated regression line is

 

Y=a+bx

 

 

Section “B”:

Question No1.

In a Honda center sales man collected spare part prices $8, $2, $14, $13, $22, $18, $30, $25, $52, $46, $63 in one day. Find out the lower quartile, upper quartile and interquartile range for the above given data.

Solution:

By arranging the data we get values

2$,8$,13$,14$,18$,22$,25$,30$,46$,52$,63$

 

Median = ?

To find median we have to see if the data number is odd or even

If it is odd then it is calculated as

Median = n+1/2

As

N=11

Median= (11+1)/2=12/2=6th value

22$

 

Lower Quartile = ?

Lower Quartile = n+1/4=(11+1)/4=12/4=3rd value

Lower Quartile = 13$

 

Upper Quartile =?

Upper Quartile =3(n+1)/4=3(12)/4=36/4=9th value

Upper Quartile = 46

 

Inter Quartile Range =?

Inter Quartile Range = Q3-Q1

Inter Quartile Range =46-13

Inter Quartile Range =33

 

 

Question No2.

Find the correlation coefficient r between variables X and Y using the following table (Do not use excel formulas to find correlation coefficient)

 

X

8

9

10

11

Y

10

5

12

11

 

ANSWER:

 

 

 

We have  to find correlation coefficient r?

 

 

So, we have to find some more values

 

 

X

Y

XY

8

10

64

100

50

9

5

81

25

45

10

12

100

144

120

11

11

121

121

121

=38

=38

=366

=390

=366

 

Putting value we get..

 

So the Correlation Coefficient is 0.41

 

 

Section “C”:

 

 

Question No 1:

 

60

80

90

96

120

150

200

360

480

520

1060

1200

1450

2500

7200

The annual incomes (in thousands of $) of fifteen families is as

 

Calculate the

  • Geometric mean

G=(x1*x2*x3*……*xn) ^1/n

 GM= (60*80*90*96*120*150*200*360*480*520*1060*1200*1450*2500*7200) ^1/15

=377.209 Ans

 

  • Harmonic mean

         HM= n / (1/x1+1/x2+.....1/xn)

                  =15/(1/60+1/80+1/90+1/96+1/120+1/150+1/200+1/360+1/480+1/520+1/1060

                       +1/1200+1/1450+1/2500+1/7200)

                  = 186.3 Ans

  • Quartile deviation

Quartile divide data into 4 equal parts.

Position of Q1= (n+1)/4 = (15+1)/4 = 16/4 = 4

                         = 4th value = 120

Position of Q2 = 2(n+1)/4 = 2(15+1)/4 = 2(16)/4 = 32/4= 8

                          = 8th value = 480

 

Position of Q3= 3(n+1)/4 = 3(15+1)/4 = 3(16)/4 = 48/4 = 12

                         = 12th value = 1450

 

 

 

 

Question 2:

 

Find the correlation between candidates score in interview and written test for a random sample of 6 candidates, which is as

 

X

2

4

5

6

8

11

Y

18

12

10

8

7

5

 

Where X=Interview marks, Y=Marks of written test.

 Solution:

 Using formula

 

X

Y

XY

2

18

4

324

36

4

12

16

144

48

5

10

25

100

50

6

8

36

64

48

8

7

64

49

56

11

5

121

25

55

 

Putting values in formula:

There is a negative correlation between interview marks and marks of the written test.

 

 

 

plzzzzzzzz send section D

 FOR MEDIAN CALULATION FIRST ARRY THE DATA

                                    2$,8$,13$,14$,18$,22$,25$,30$,46$,52$,63$

N=11       ,SO, ODD VAULE FOR MEDIAN =

Median= =

22$

FOR:

Lower Quartile = ?

Lower Quartile =   =          Lower Quartile = 13$

 

Upper Quartile = ?

Upper Quartile =3 =

Upper Quartile = 46$

 

Inter Quartile Range = ?

Inter Quartile Range = Q3-Q1

Inter Quartile Range  =33$

 

2nd answer

So, find the vaule is that

X


Y








XY



8


10


64


100


50



9


5


81


25


45



10


12


100


144


120



11


11


121


121


121



=38


=38


=366


=390


=366





 

 

 

Putting value we get..

    ,

   ,  ,  ,r=    

 is 0.41 Correlation Coefficient

SECTION D KAHA THA YEH KIA HAI ?

SECTION D ???????

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