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Assignment #  3

MTH302 (Spring 2015)

 

       Total marks: 10

       Lecture # 23 to 30

       Due Date: July 31, 2015

          

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Section A

Question 1:

 

 

(i)                 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 9,10,9,8,7,5,3,9,8,8,7,5,5,5,5,3,2,2,3,1,1,2,3,3,2,1,6,7,8,3.

 

(ii)               Find first second and third quartile of the following data

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

 

 

Question 2:

 

 

Find the slope of the regression line “Y = a + bX” with the help of the following data:

X

4

3

5

7

Y

7

8

9

12

Section B

Question 1:

 

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.

 

Question 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

8

9

10

11

Y

10

5

12

11

 

 

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.

 

 

Section D

Question 1:

A company expenditures on advertising (in hundreds of $) are as follows:

 

X

15

20

22

11

27

18

33

12

14

27

10

 

Find

1)      Range

2)      Mid Range

3)      Median

4)      Mode

Question 2:

 

From the data ‘x’ values 22, 35, 38, 33, 28, 37, 40, 20, 26, calculate

1)      Mean deviation

2)      Variance

 

 

 

 

 

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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.

 

Solution:

As  

Here,

 For Harmonic mean

 

So, in this case

For Quartiles,

 

Hence Quartile deviation is

 

 

 

 

 

 

 

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:

 

In order to compute the correlation coefficient, we carry out the following calculations

 

X

Y

X2

Y2

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

∑X=36

∑Y=60

∑X2=266

∑Y2=706

∑XY=293

 

 

Section D

Question 1:

A company expenditures on advertising (in hundreds of $) are as follows:

 

X

15

20

22

11

27

18

33

12

14

27

10

 

Find

1)      Range

2)      Mid Range

3)      Median

4)      Mode

Solution:

 

Arrange the data in ascending order

X

10

11

12

14

15

18

20

22

27

27

33

Maximum Value = =33

Minimum Value = =10

1)      Range =-=33-10 = 13

2)      Mid Range =  =13/2 = 6.5

3)      Median = (n+1/2 )th item = (11+1)/2 th item  = 6th item = 18

4)      Mode = Most frequent value  = 27

 

Question 2:

 

From the data ‘x’ values 22, 35, 38, 33, 28, 37, 40, 20, 26, calculate

1)      Mean deviation

2)      Variance

Solution:

 

 

22

-9

9

81

35

4

4

16

38

7

7

49

33

2

2

4

28

-3

3

9

37

6

6

36

40

9

9

81

20

-11

11

121

26

-5

5

25

 279

 =0

 =56

=422

 

 

1)      Mean Deviation =

2)      Variance =

 

 

 

 

 

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