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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 Views: 3085

### Replies to This Discussion

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 =