MCom I Semester Statistical Analysis Interpolation Extrapolation Study Material Notes ( Part 2 )
Table of Contents
MCom I Semester Statistical Analysis Interpolation Extrapolation Study Material Notes ( Part 2 ) : Table Showing advancing Differences Interpolation and extrapolation in continuous Frequency Distribution Lagrange Method Interpolation in Continuous Frequency Distribution Newton Gauss Backward Method Newon Method For Divided Differences Long Answer Questions Short Answer Questions Numericals :
CTET Paper Level 2 Questions Answer Language II English Model paper
Illustration 13.
The following table gives the population of a district for various years. Find out the population for the year 1985.
|
Year |
1961 | 1971 | 1981 | 1991 | 2001 |
| Population in Lakh) : | 70 | 90 | 360 | 140 |
160 |
It becomes clear from the given data of population that there is sudden ups in the population of 1981. Hence, the population of 1981 would be assumed as unknown. So, first of all we will interpolate the population of 1981. After that, replacing the such interpolated value we will find out the population for the year 1985. It should also be noted that we will use the Binomial Expansion Method for interpolating the population of 1981 and Newton’s Method of Advancing Differences for the population of 1985.
Interpolation for 1981 :
x : 1961 (x) 1971 (x) 1981 (1) 1991 (x3) 2001 (*)
y : 70 V) 90 (1) ? () 140 (3) 160 (4)
Since the known values are four, the fourth leading difference will be zero i.e., (y – 1) = 0 or Aj = 0. Therefore, we will use the following equation to find out the estimated population for the year 1981 :
EXAMINATION QUESTIONS
Long Answer Theoretical Questions
1 Describe the utility of interpolation and extrapolation for a businessman. Explain the various methods of interpolation.
2. Describe briefly any three methods of estimating a missing figure in a time series. Give circumstances in which cache of them can most suitably be used and the assumption made there in
3. What are the assumptions generally made in interpolation and extrapolation ? Mention the chief methods used for this purpose giving the conditions under which they are suitable.
4. Discuss the utility of interpolation and extrapolation to a businessman. What are the different methods known to you for interpolation ?
5. What do you mean by interpolation and extrapolation ? How far interpolated or extrapolated values can be relied upon ?
6. What do you understand by ‘Interpolation and extrapolation’? Explain with example the procedure of Extrapolation by Newton-Gauss Backward Method.
7. Explain the meaning of interpolation. How does it differ from forecasting ? Discuss its importance in commerce and industry.
Short Answer Questions
1 What do you mean by Interpolation ?
2. What do you mean by Extrapolation ?
3. Differentiate between Interpolation and extrapolation.
4. Write down two assumptions underlying Interpolation and Extrapolation.
5. On what two factors does the accuracy of Interpolation and extrapolation depend ?
6. Construct Pascal’s Triangle up to n = 8.
7. Write down Newton’s Advancing Differences Formula up to Af for interpolating ye
8. In a case of equal intervals of items of x, four values of y are known and two values of y are to be interpolated, write down two equations to be used for solution.
9. In a case of unequal intervals of r, three values of y are known and one has to be interpolated, write down Lagrange’s formula to be used.
10. Give the table of differences under Newton’s Advancing Differences Method up to the fourth leading difference (A3).
11. Explain in brief the Binomial Expansion method of Interpolation.
12. Explain in brief Newton’s Advancing Differences.
13. Explain in brief Lagrange’s Method of Interpolation.
14. Explain in brief the Parabolic Curve Method of Interpolation.
15. What are the two essential conditions that must be satisfied for the application of the Binomial Expansion Method.
16. Describe the Graphic Method of Interpolation.
Objective Type Questions
State whether the following statements are true or false :
1 We should kept in mind the assumptions while making interpolation and extrapolation.
(True)
2. Lagrange method is used only when equal difference is found in values of independent variable ‘r.
(False)
3. Binomial expansion method applies for interpolation when dillerence between values of independent variable is not equal.
(False)
4. Interpolation and Extrapolation assume that there are not wide fluctuations in the available data.
(True)
5. Power in a parabolic curve equation extend upto total number of known values.
(False)
Interpolation Extrapolation Study Material
6. A technique of estimating a past figure is termed as Extrapolation. (False) 7. Ir known values are seven, then the equation of Binomial Expansion will be : y7 – 7y6 + 2 lys – 65y4 + 35y3 – 21y2 + 7y1 – yo = 0
(False)
7. If known values are five, then number of advancing differences would be five.
(False)
Fill in the blanks :
1 We should kept in mind the ……… while making interpolation and extrapolation.
2. There should be no ……… in the period of known data.
3. Binomial expansion method is based on ………. of Algebra.
4. When there is sudden fluctuation in the given values, then before finding the ………, we should interpolate the ………..
5. ………. in interpolation is also known as the method of simultaneous equations.
6. ……… method of interpolation can be used to interpolate in all conditions.
7. ………. means a value that lies outside two extreme points.
8. Lagrange’s formula is applicable in those cases where x variable advances by ..
9. A technique of estimating a past figure is termed as ……….
10. The binomial distribution is associated with the name of ………. mathematician.
Ans. (1) Assumptions, (2) Fluctuation, (3) Binomial Theorem, (4) Unknown Value, Fluctuated Value, (5) Parabolic Curve Method, (6) Lagrange, (7) Extrapolation, (8) Either regular or irregular, (9) Interpolation, (10) Swiss,
Select the Correct Option :
1 Binomial expansion method is used for interpolation or extrapolation, where the differences in the values of the independent variable are:
(a) Equal (V)
(b) Not Equal
(c) Increasing
(d) Decreasing
2. Value that lies outside two extreme points is known as:
(a) Interpolation
(b) Extrapolation (V)
(c) Estimation
(d) Correlation
3. For interpolation or extrapolation, the class intervals are converted into cumulative frequency series :
(a) In the Binomial Expansion Method
(b) In Newton’s Method of Advancing Differences
(C) In Lagrange Method
(d) In both Newton and Lagrange Method (V)
4. If there is not an equal difference in the different values of the independent variable, then for interpolation and extrapolation, we will use :
(a) Binomial Expansion Method
(b) Newton’s Method of Advancing Differences
(C) Lagrange Method (v)
(d) None of these
5. If value of dependent variable for items of independent variable at equal difference is given, then to find out the value of any such item of independent variable which is not lies on equal difference, we will use :
(a) Binomial Expansion Method
(b) Newton’s Method of Advancing Differences (V)
(c) Lagrange Method
(d) None of these
6. Lagrange’s formula is applicable where x variable advances by :
(a) Regular Interval
(b) Irregular Interval (V)
(C) Both of the above
(d) None of these
7. When the population of 1995, 1996, 1997 and 1999 years are known then to estimate the population of 1998 we will use :
(a) Binomial Method (V)
(b) Newton’s Method
(c) Lagrange Method
(d) None of these
8. If the sales for the years 1980, 1985, 1990 and 1995 has been given, then to find out the sales of 1992, we will use :
(a) Lagrange Method
(b) Binomial Method
(C) Newton’s Method (V)
(d) None of these
9. Binomial expansion method is applicable where x’ variable advances by :
(a) Regular Interval (V)
(b) Irregular Interval
(C) Both of the above
(d) None of these
10. If the national income for the years 1980, 1985, 1988 and 1995 has been given then to find out the national income of 1990, we will use :
(a) Binomial Method
(b) Lagrange Method (V)
(C) Newton’s Method
(d) None of these
11. If X0,X, X, and x, are 20, 25, 30 and 28 respectively, then x would be:
(a) 0.6
(b) -0,6
(C) 1.6 (V)
(d) None of these
12. If known values of y’ variable are five, then the number of advancing differences will be :
(a) 5
(b) 4 (V)
(d) None of these
(C) 6
Interpolation Extrapolation Study Material
