P-8: Fitting of Power and Exponential Curves

 

PRACTICAL EXERCISE – 8

Fitting of Power Curve and Exponential Curves

1. The following table gives corresponding values of two variables X and Y. Fit power curve to the given data.

x	y
1	1.8
2	5.1
3	8.9
4	14.1
5	19.8

 

2. Fit an exponential curve of the form  y=ab power x    to the following data.

x	y
1	1.0
2	1.2
3	1.8
4	2.5
5	3.6
6	4.7
7	6.6
8	9.1

 

3.  For the data given below, find the equation to the best fitting exponential curve of the form y=a e power x.

x	y
1	1.6
2	4.5
3	13.8
4	40.2
5	125.0
6	300.0

P-7: Fitting of St. Line and Second degree Parabola

 

PRACTICAL EXERCISE – 7

Fitting of Straight Line and Second-Degree Parabola

 

1.     The weights of the calf taken at weekly intervals are given below. Fit a straight line using the method of least squares and calculate the average rate of growth per week.

Age (X)	1	2	3	4	5	6	7	8	9	10
Weight (Y)	52.5	58.7	65	70.2	75.4	81.1	87.2	95.5	102.2	108.4

 

2.     Fit a straight line to the following data

x	1	2	3	4	5	6	7	8
y	55	46	40	38	33	30	29	30

 

3.     Fit a parabola of second degree to the following data.

x	0	1	2	3	4
y	1	1.8	1.3	2.5	6.3

 

4.     Fit a second-degree curve to the following data relating to profit of certain company. Estimate the profit in the year 1995.

Year	1980	1982	1984	1986	1988
Profit ( In Rs. Lakhs)	125	140	165	195	230

 

 

COMPUTATION OF KARL PEARSON’S COEFFICIENT OF SKEWNESS AND BOWLEY’S COFFICIENT OF SKEWNESS

 

PRACTICAL EXERCISE -6

COMPUTATION OF KARL PEARSON’S COEFFICIENT OF SKEWNESS AND BOWLEY’S COFFICIENT OF SKEWNESS

1. Obtain Karl Pearson’s measure of skewness for the following data

Value	Frequency
5-10	6
10-15	8
15-20	17
20-25	21
25-30	15
30-35	11
35-40	2

 

2. Assume that a firm has selected a random sample of 100 from its production line and has obtain the data in the table below:

Class Interval	Frequency
130-134	3
135-139	12
140-144	21
145-149	28
150-154	19
155-159	12
160-164	5

 

Compute the (a). Karl Pearson’s coefficient of skewness (b). Bowley’s coefficient of skewness.

 

3. For the frequency distribution given below, calculate the coefficient of skewness based on quartiles.

Annual sales	No. of Firms
Less than 20	30
Less than 30	225
Less than 40	465
Less than 50	580
Less than 60	634
Less than 70	644
Less than 80	650
Less than 90	665
Less than 100	680