Course : US04FBCA01
(Computer Based Numerical and Statistical Methods)
Question Bank
Unit-1
MCQ1 / f(a) < 0, f(b) > 0 and if x0 Є (a,b)is first approximation with f(x0) < 0 then in bisection method,
(a) x0 is to be replaced by a (b) ais to be replaced by c
(c) bis to be replaced by x0 (d) x0 is to be replaced by b
2 / For real root of an equation x3-2x-5=0, the root lies between
(a) 0 and 1 (b) 2 and 3 (c) 1 and 2 (d)none of them
3 / From the following ______method is not iterative method.
(a) False position (b) Bisection (c) Lagranges (d)none of them
4 / For the function f(x):x3-2x-5 = 0 if the root of equation lies between (2,3) and if at ith iteration c=2.5 then next approximation by bisection method is given c=
(a) (b) (c) (d) none of them
5 / If in a method of successive approximation, the root of equation lies between 1 and 2, , and initial guess is 1.25 then next approximation is
(a) 0.5625 (b) 1.2177 (c) 1.7777 (d)none of them
6 / From the following ______method is the best method to obtain root of equation f(x)=0.
(a) False position (b) Bisection (c) Newton’s Raphson (d)none of them
7 / True error is defined as
(a) Present Approximation – Previous Approximation
(b) True Value – Approximate Value
(c) abs (True Value – Approximate Value)
(d) abs (Present Approximation – Previous Approximation)
8 / The number 0.01850 x 103 has _000______significant digits
(a) 3 (b) 4 (c) 5 (d) 6
9 / For an equation like x2=0, a root exists at X=0. The bisection method cannot be adopted to solve this equation in spite of the root existing at x=0 because the function f(x) =x2
(a) is a polynomial (b) has repeated roots at x= 0
(c) is always non-negative (d) has a slope equal to zero at x= 0
10 / If for a real continuous function f(x), f(a)f(b)<0, then in the range of [a,b] for f(x)=0, there is (are)
(a) one root (b) an undeterminable number of roots
(c) no root (d) at least one root
Answers of MCQ
1.(b), 2.(b), 3.(c), 4.(b), 5.(c), 6.(c), 7.(b), 8.(d), 9.(c), 10.(d)
Short questions
1
2 / Define Relative error and absolute error.
3 / Describe the stopping rules to obtain approximate solution for given non-linear equations.
4 / Use the False Position method to obtain approximate solution of the equation X3-9x+1=0.
5 / Use the secant method to obtain approximate solution of the equation X3-5x-3=0. [initial approx. 2 & 3 ans: 0.656]
6 / Use the Successive approximation method to obtain approximate solution of the equation 2x-x-3=0 with interval [-3,-2] and correct to four decimal places. [initial approx. -3
Long Questions
1 / Write algorithm for bisection method.
2 / Write algorithm for RegulaFalsi method.
3 / Write algorithm for iterative method.
4
5 / Define Relative error and absolute error.
6 / Bisection method
7 / RegulaFalsi OR False position method
8 / Secant method
9 / Iterative method
Take a=-3
Take a=1.5
Unit 2
MCQ1 / Theile defines ______as “the art of reading between the lines of a table.”
(a)Extrapolation (b) Divided difference (c) Lagrange’s (d) Interpolation
2 / All the formulae of interpolation are based on the fundamental assumption that the given data can be expressed as a ______.
(a) Polynomial (b) Equation (c) Algorithm (d) None of the above
3 / ______method is used if the estimated value lies towards the end of the difference table.
(a)Divided difference (b) Forward difference (c) Backward difference (d) None of the above
4 / y depends on x can be written as ______
(a)f(x) or yx (b) f(xy) (c) f(yx) (d) none of the above
5 / ______method of interpolation is used for unequally spaced functions.
(a) Forward difference (b) backward difference
(c) Newton’s divided difference(d) None of the above
6 / To estimate the value of dependent variable x for a given value of independent variable y, the process is known as ______.
(a)Extrapolation (b) Inverse Interpolation (c) Interpolation (d) polynomial
7 / ______is called the forward difference operator.
(a) (b) (c) (d)
8 / ______is called the backward difference operator.
(a) (b) (c) (d)
9 / The main disadvantage of Lagrangian interpolation is that it is difficult to find the order of the ______to be fitted.
(a) Polynomial (b) Equation (c) Algorithm (d) None of the above
10 / ______is not a type of interpolation method.
(a) Forward difference (b) backward difference
(c) Newton’s divided difference(d) moving average method
11 / The formula for inverse interpolation is obtained from ______interpolation formula by changing the variable x and y=f(x).
(a) Forward difference (b) backward difference
(c) Newton’s divided difference(d) Lagrangian
12 / The second order differences is denoted by ______.
(a) (b) (c) (d)
13 / If population census for the years 1931, 1941, 1951, 1961 and 1971 is given and if we want to estimate the population for the year 1935 then ______method is used.
(a) Forward difference (b) backward difference
(c) Newton’s divided difference(d) Lagrangian
14 / If the argument for the interpolation is not an equidistant then which method of interpolation is most appropriate.
(a) Forward difference (b) backward difference
(c) Newton’s divided difference(d) all of the above
15 / The estimate obtained by interpolation method is always accurate or reliable.
(a)true (b) false (c) Not applicable
Answers of MCQ:
1.(d), 2.(a), 3.(c), 4.(a), 5.(c), 6.(b), 7.(a), 8.(b), 9.(a), 10.(d),
11.(d), 12.(b), 13.(a), 14.(c), 15.(b)
Short Questions
1 / Define Interpolation.
2 / Define Extrapolation.
3 / Write algorithm for forward difference table.
4 / Write algorithm for Backward difference table.
5 / Write different methods of Interpolation.
6 / Draw forward difference table.
7 / Draw backward difference table.
8 / Explain forward difference method.
9 / Explain backward difference method
10 / Explain central difference method.
11 / Explain divided difference method.
12 / Explain Lagrangian method.
Long Questions
Example on Interpolation
Forward and Backward Difference
1 / If y= 2x3 – x2 + 3x +1, calculate the value of y corresponding to x = 0, 1, 2, 3, 4, 5 and form the table of differences.
2 / Estimate the expectation of life at the age of 16 years by using the following data:
Ans: 31.7 years
Age (In Years) / 10 / 15 / 20 / 25 / 30 / 35
Expectation of life (In Year) / 35.4 / 32.3 / 29.2 / 26.0 / 23.2 / 20.4
3 / The following results are given. Using them find
Ans: 2.962
4 / Using an appropriate formula for interpolation estimate the no. of students who obtained < 45 marks from the following. Ans: 48
Marks / 0-40 / 40-50 / 50-60 / 60-70 / 70-80
No. of students / 31 / 42 / 51 / 35 / 31
5 / From the following table find the no. of workers falling in the earning group of Rs. 25 to Rs. 35. Ans: y35 – y25 = 396 – 218 = 178
Earning (Rs.) / Up to 10 / Up to 20 / Up to 30 / Up to 40 / Up to 50 / Up to 60
No. of Workers / 50 / 150 / 300 / 500 / 700 / 800
6 / If Lx represents the numbers living at age x in a life table interpolate, by using newton’s method of Lx for the values of x = 24 and x= 29. ( Ans: L24 = 486 , L29 = 447)
L20 = 512, L30= 439, L40 = 346, L50 = 243
7 / The following table gives the census population of a town for the years 1931 to 1971. Estimate the population for the year 1965 by using an appropriate interpolation formula.
Ans: 96.834
Year / 19931 / 1941 / 1951 / 1961 / 1971
Population / 46 / 66 / 81 / 93 / 101
8 / Estimate by Newton’s method of interpolation, the expectation of life at age 32 from the following table. Ans: 22.0948
Age (In Years) / 10 / 15 / 20 / 25 / 30 / 35
Expectation of life (In Year) / 35.3 / 32.4 / 29.2 / 26.1 / 23.2 / 20.5
9 / By Newton’s or by any other algebraic method find the no. of persons who probably will be travelling if rate is 4.2. Ans : 49,712
Rate / 5.0 / 4.5 / 4.0 / 3.5 / 3.0
Passengers / 30,000 / 40,000 / 60,000 / 1,00,000 / 1,50,000
10 / Given the table of values as
x / 2.0 / 2.25 / 2.50 / 2.75 / 3.0
y(x) / 9.00 / 10.06 / 11.25 / 12.56 / 14.00
Find y(2.35). Ans: 10.522
11 / Given the table of values as
X / 2.5 / 3.0 / 3.5 / 4.0 / 4.5
y(x) / 9.75 / 12.45 / 15.70 / 19.52 / 23.75
Find y(2.35). Ans: 21.601
Divided Difference Method
12 / The observed values of a function are respectively 168, 120, 72, 63 at the four positions 3, 5, 9, 10 of the independent variable. What is the best estimate you can give for the value of the function at the position 6 of the independent variable? Ans: 147
13 / From the following table find the function f(x) assuming it to be a polynomial of 3rd degree in x. Ans: x3 + x2 – x + 1
x / 0 / 1 / 2 / 3
f(x) / 1 / 2 / 11 / 34
14 / Apply Newton’s divided difference method to find the no. of persons getting Rs. 6 from the following data. Ans: 135
Income per day / 3 / 5 / 7 / 8 / 10
No. of persons / 180 / 154 / 120 / 110 / 90
15 / Given the table of values as (use divided difference method)
x / 2.5 / 3.0 / 3.5 / 4.75 / 6.0
y(x) / 8.85 / 11.45 / 20.66 / 22.85 / 38.60
Find y(2.35). Ans: 13.993
Lagrangian method
16 / Given the table of values as (use Lagrangian method)
x / 0 / 1 / 2 / 3
y(x) / 0 / 2 / 8 / 27
Find y(2.35). Ans: 15.313
17 / Find the polynomial function f(x) given that f(0) = 2, f(1) = 2 , f(2) = 12 and f(3)= 35 find f(5). Ans: 147
18 / By using Lagrange’s method, estimate the no. of persons whose income is Rs. 19 and more but does not exceed Rs. 25 from the following table.Ans: y25 – y19 = 228– 120 = 108
Income in Rs. / 1 and not exceeding 9 / 10 and not exceeding 19 / 20 and not exceeding 28 / 29 and not exceeding 37 / 38 and not exceeding 46
No. of persons / 50 / 70 / 203 / 406 / 304
19 / Given a function in the form of a table as
x / 2.0 / 3.0 / 4.0
y(x) / 6.6 / 9.2 / 8.6
Interpolate the value of y(x) using Lagrangian polynomial at x= 2.8 and x= 3.
20 / Inverse Interpolation
The value of x and y= f(x) are given below
x / 5 / 6 / 9 / 11
f(x) / 12 / 13 / 14 / 16
Find value of x when f(x)= 15. Ans: 11.5
21 / Explain Interpolation and extrapolation.
22 / Explain Lagrangian method.
23 / Explain forward difference and backward difference methods.
24 / Explain divided and central difference method.
Unit 3
MCQ
1 / We can find solution of system of linear, algebraic equations using………
(a) Newton-Raphson method (b) Bisection method
(c) Gauss-Seidel method (d) None of these
2 / The system of linear equation AX = B can be solved by matrix inversion method only if…
(a) (b) (c) (d) A is symmetric
3 / The system of linear equation AX = B can be solved by Gauss-Seidel method only if…
(a) All diagonal elements of A are zero (b) All diagonal elements of A are non zero
(c) All diagonal elements of A are dominant (d) A is skew symmetric
4 / The system of linear equation AX = B is said to be homogeneous if…
(a) (b) B = 0 (c) A = 0 (d) A is symmetric
5 / The system of linear equation AX = B is said to be non-homogeneous if…
(a) (b) B = 0 (c) (d) A is symmetric
6 / Rate of change of distance with respect to time reprents….
(a) Acceleration (b) Speed (c) Pressure (d) None of these
7 / For equally spaced tabular values, the Newton’s forward interpolation formula can be used to find derivative at a point x if…..
(a) x is in the upper half of the table (b) x is in the lower half of the table
(c) x is at the center of the table (d) None of these
8 / Consider the following system of linear equation
3x + y – z = 10, x + 5y + 2z = 18, x + 4 y + 9z = 16
If current approximation is x = 3.33, y = 2.93, z= 0.1, then the Gauss-Seidel method will give next approximation as x = 2.39, y = 3.08 and z =
(a) 1.2 (b) 0.21 (c) 0.14 (d) 0.19
9 / Consider the following system of linear equation
3x + y + z = 0, x + 4y – z = 1, 2x – y + 5z = 2
If current approximation is x = 0, y = 0.25, z= 0.45, then the Gauss-Seidel method will give next approximation as x = – 0.23, y = 0.42 and z =
(a) 0.58 (b) 0.48 (c) 0.7 (d) 0.24
Answers of MCQ:
1(c), 2(b), 3(c), 4(b), 5(a), 6(b), 7(a), 8(a), 9(c)
Short Questions
1 / Solve the following system of equations.
(a) 2x + 3y = –10 (b) 10x + 3y = 5
–x + 4y = –4 8x – 2y = 2
(c) 2x + 3y = 1 (d) 2x – y = 4
–x + 2y = 8 x + 9y = –8
2 / List only various direct and iterative methods.
3 / If x lies in the upper half of the table and if , then what is and ?
4 / If x lies in the upper half of the table and if , then what is and ?
5 / If x lies in the lower half of the table and if , then what is and ?
6 / If x lies in the lower half of the table and if , then what is and ?
Long Questions
1 / Solve the following system of equations using matrix inversion method. (can be asked to write in matrix form as short question)
(i) (ii) (iii)
(iv) (v)
2 / Solve the following system of equations using Gauss-Seidel method.
(i) (ii) (iii)
(iv) (v) vi)
3 / Explain the matrix inversion method for solution of system of linear equations.
4 / Explain the Gauss-Seidel method for solution of system of linear equations.
5 / Write the comparison between direct and iterative methods for solution of system of linear equations.
6 / Given the following table
/ 0.50 / 0.75 / 1.00 / 1.25 / 1.50
/ 0.13 / 0.42 / 1.00 / 1.95 / 2.35
Find and .
7 / The distance (s) covered as a function of time (t) by an athlete during his/her run for the 50 meter race is given in the following table
Time(Secs.) / 0 / 1 / 2 / 3 / 4 / 5 / 6
Distance(Mts.) / 0 / 2.5 / 8.5 / 15.5 / 24.5 / 36.5 / 50
Determine the speed of the athlete at t = 5 and t = 4.5 seconds.
8 / The distance (s) covered by a car in given time (t) is given in the following table
Time(Minutes) / 10 / 12 / 14 / 16 / 18
Distance(km) / 12 / 15 / 20 / 27 / 37
Determine the speed of the car at t = 13 minutes.
9 / The distance (s) covered by a car in given time (t) is given in the following table
Time(Miutes) / 10 / 12 / 14 / 16 / 18
Distance(km) / 12 / 15 / 20 / 27 / 37
Determine the acceleration of the car at t = 13 minutes.
10 / Given the following table
/ 0 / 1 / 2 / 3 / 4 / 5 / 6
/ 0 / 2 / 2.75 / 3.4 / 3.2 / 2.5 / 2.2
Use forward difference formula to compute at 2.25.
11 / Given the following table
/ 0 / 1 / 2 / 3 / 4 / 5 / 6
/ 0 / 2 / 2.75 / 3.4 / 3.2 / 2.5 / 2.2
Use backward difference formula to compute at 6.
12 / The pressure of a certain gas was recorded at intervals of two seconds, and the results are listed in the following table:
Time(t) / 0 / 2 / 4 / 6 / 8
Pressure(p) / 50 / 53 / 57 / 68 / 82
Estimate the rate of change of pressure at t = 2.5.
13 / Given the following table
/ 3 / 4 / 5 / 6 / 7 / 8
/ 4 / 6.6 / 7.7 / 9.0 / 10.5 / 12.2
Use backward difference formula to compute at x = 7 and x = 7.5.
14 / Given the following table
/ 10 / 11 / 12 / 13 / 14
/ 15 / 12.8 / 10.6 / 8.5 / 6.4
Estimate the value of and at 10, 10.5, 11, 11.2 using the forward difference formula.
Unit 4
MCQ
1 / Forecasts ______.
a. become more accurate with longer time horizons
b. are rarely perfect
c. are more accurate for individual items than for groups of items
d. all of the above
2 / One purpose of short-range forecasts is to determine ______.
a. production planning
b. inventory budgets
c. facility location
d. job assignments
3 / Forecasts are usually classified by time horizon into three categories ______.
a. short-range, medium-range, and long-range
b. finance/accounting, marketing, and operations
c. strategic, tactical, and operational
d. exponential smoothing, regression, and time series
4 / A forecast with a time horizon of about 3 months to 3 years is typically called a ______.
a. long-range forecast
b. medium-range forecast
c. short-range forecast
d. weather forecast
5 / Gradual, long-term movement in time-series data is called ______.
a. seasonal variation
b. cycles
c. trends
d. exponential variation
6 / A time series is a set of data recorded______.
a. periodically
b. at time or space intervals
c. at successive points of time
d. all the above
7 / The time series analysis helps:
a. to compare the two or more series
b. to know the behavior of business
c. to make predictions
d. all the above
8 / A time series consists of:
a. two components
b. three components
c. four components
d. five components
9 / The component of a time series attached to long-term variations is term as:
a. Cyclic Variations
b. Secular Trend
c. Irregular Variation
d. all of the above
10 / The component of a time series which is attached to short-term fluctuations is:
a. seasonal variation
b. cyclic variation
c. irregular variation
d. all of the above
11 / A lock-out in a factory for a month is associated with the component of a time series:
a. irregular movement
b. secular trend
c. cyclic variation
d. none of the above
12 / The general decline in sales of cotton clothes is attached to the component of the time series:
a. secular trend
b. cyclical variation
c. seasonal variation
d. all of the above
13 / The sales of departmental store on Dushera and Diwali are associated with the component of a time series:
a. secular trend
b. seasonal variation
c. irregular variation
d. all the above
14 / The consistent increase in production of cereals constitutes the component of a time series:
a. secular trend
b. seasonal variation
c. cyclical variation
d. all the above
15 / Secular trend is indicative of long-term variation towards:
a. increase only
b. decrease only
c. either increase or decrease
d. none of the above
16 / Linear trend of a time series indicates towards:
a. constant rate of change
b. constant rate of growth
c. change in geometric progression
d. all the above
17 / Seasonal variation means the variation occurring within:
a. a number of years
b. parts of a year
c. parts of a month
d. none of the above
18 / Salient factors responsible for seasonal variation are:
a. weather
b. social customs
c. festivals
d. all the above
19 / Cyclic variations in a time series are caused by:
a. lockouts in a factory
b. war in a country
c. floods in the states
d. none of the above
20 / Irregular variations in a time series are caused by:
a. lockouts and strikes
b. epidemics
c. floods
d. all the above
21 / In ratio to moving average method for seasonal indices, the ratio of an observed value to the moving average remove the influence of:
a. trend
b. cyclic variation
c. trend and cyclic variation both
d. none of these
22 / The moving averages in a time series are free from the influences of:
a. seasonal and cyclic variations
b. seasonal and irregular variations
c. trend and cyclical variations
d. trend and random variations
Answers of MCQ
1.(b), 2.(d), 3.(a), 4.(b), 5.(c), 6.(d), 7.(d), 8.(c), 9.(b), 10.(d), 11.(a), 12.(a), 13.(b), 14.(a), 15.(c), 16.(a), 17.(b), 18.(d), 19.(d), 20.(d), 21.(c), 22.(b)
Short Questions
1 / What is Time Series?
2 / What do you mean by Secular trend?
3 / Differentiate between linear and nonlinear trend.
4 / What time series analysis consists?
5 / List the utilities of time series.
6 / List the component of Time series.
7 / What do you mean by Cyclic Variation?
8 / What do you mean by random or irregular Variation?
9 / Write objectives for studying seasonal pattern in time series.
10 / Write limitation of Simple Average Method.
11 / Write merits and demerits of ‘Ratio to Moving Average’ method.
12 / Write a note on Forecasting by the use of Time Series Analysis.
13 / Write a note on Casual Model of Forecasting.
14 / Write a note on Survey Method of Forecasting.
Long Questions
1 / Calculate three yearly moving averages for the following data
YEAR / 1950 / 1951 / 1952 / 1953 / 1954 / 1955 / 1956 / 1957 / 1958 / 1959 / 1960
Y / 242 / 250 / 252 / 249 / 253 / 255 / 251 / 257 / 260 / 265 / 262
2 / Calculate the trend values by the method of moving average, assuming a four-yearly cycle from the following data relating to sugar production in India.
YEAR / SUGAR PRODUCTION
(lakh tones) / YEAR / SUGAR PRODUCTION
(lakh tones)
1971 / 37.4 / 1977 / 48.4
1972 / 31.1 / 1978 / 64.4
1973 / 38.7 / 1979 / 58.4
1974 / 39.5 / 1980 / 38.6
1975 / 47.9 / 1981 / 51.4
1976 / 42.6 / 1982 / 84.4
3 /
- Obtain the trend from the time series given below by method of moving average of [i] 3 years [ii] 5 years
Y / 500 / 540 / 550 / 530 / 520 / 560 / 600 / 640 / 620 / 640
4 /
- Obtain the trend from the time series given below by method of moving average of 4 years
Y / 50.0 / 36.5 / 43.0 / 44.5 / 38.9 / 38.1 / 32.6 / 41.7 / 41.1 / 33.8
5 /
- Obtain seasonal indices using simple average method.
1 / 30 / 81 / 62 / 119
2 / 33 / 104 / 86 / 171
3 / 42 / 153 / 99 / 221
4 / 56 / 172 / 129 / 235
5 / 67 / 201 / 136 / 302
6 /
- Obtain seasonal indices using simple average method.
1974 / 30 / 81 / 62 / 119
1975 / 33 / 104 / 86 / 171
1976 / 42 / 153 / 99 / 221
1977 / 56 / 172 / 129 / 235
7 /
- Obtain seasonal indices using ratio to moving average.
1970 / 25 / 30 / 21 / 32
1971 / 27 / 28 / 25 / 34
1972 / 22 / 27 / 21 / 30
1973 / 24 / 25 / 20 / 33
8 /
- Obtain seasonal indices using ratio to moving average.
1990 / 30 / 40 / 36 / 34
1991 / 34 / 52 / 50 / 44
1992 / 40 / 58 / 54 / 48
1993 / 54 / 76 / 68 / 62
9 / Use the method of monthly averages to determine the monthly indices for the following data of production of a commodity for the year 1979, 1980, 1981.
MONTH / 1979 / 1980 / 1981
(Production in lakhs of tones)
JANUARY / 12 / 15 / 16
FEBRUARY / 11 / 14 / 15
MARCH / 10 / 13 / 14
APRIL / 14 / 16 / 16
MAY / 15 / 16 / 15
JUNE / 15 / 15 / 17
JULY / 16 / 17 / 16
AUGUST / 13 / 12 / 13
SEPTEMBER / 11 / 13 / 10
OCTOBER / 10 / 12 / 10
NOVEMBER / 12 / 13 / 11
DECEMBER / 15 / 14 / 15
10 / Calculate seasonal indices by ‘ratio to moving average method’ for the following data.
YEAR / I Quarter / II Quarter / III Quarter / IV Quarter
1971 / 68 / 61 / 61 / 63
1972 / 65 / 58 / 66 / 61
1973 / 68 / 63 / 63 / 67
11 / Calculate the seasonal indices by the ‘ratio to moving average’ method from the following.
Year / Quarter / Y / 4-Quarterly Moving Average
1972 / I / 75 / -
II / 60 / -
III / 54 / 63.375
IV / 59 / 65.375
1973 / I / 86 / 67.125
II / 65 / 70.875
III / 63 / 74.000
IV / 80 / 75.375
1974 / I / 90 / 76.625
II / 72 / 77.625
III / 66 / 79.500
IV / 85 / 81.500
1975 / I / 100 / 83.000
II / 78 / 84.750
III / 72 / -
IV / 93 / -
12 / The number (in hundreds) of letters posted in certain city on each day in a typical period of five weeks was as follows. Find the seasonal indices by simple average method.
Week / Sun. / Mon. / Tue. / Wed. / Thu. / Fri. / Sat.
1st / 18 / 161 / 170 / 164 / 153 / 181 / 76
2nd / 18 / 165 / 179 / 157 / 168 / 195 / 85
3rd / 21 / 162 / 169 / 153 / 139 / 185 / 82
4th / 24 / 171 / 182 / 170 / 162 / 179 / 95
5th / 27 / 162 / 186 / 170 / 170 / 182 / 120
13 / Compute the seasonal average and seasonal indices for the following time-series.
Month / 1974 / 1975 / 1976 / Month / 1974 / 1975 / 1976
JANUARY / 15 / 23 / 25 / JULY / 20 / 22 / 30
FEBRUARY / 16 / 22 / 25 / AUGUST / 28 / 28 / 34
MARCH / 18 / 28 / 35 / SEPTEMBER / 29 / 32 / 38
APRIL / 18 / 27 / 36 / OCTOBER / 33 / 37 / 47
MAY / 23 / 31 / 36 / NOVEMBER / 33 / 34 / 41
JUNE / 23 / 28 / 30 / DECEMBER / 38 / 44 / 53
14 / Calculate the seasonal index from the following data using the simpleaverage method.
Year / 1st Quarter / 2nd Quarter / 3rd Quarter / 4th Quarter
1974 / 72 / 68 / 80 / 70
1975 / 76 / 70 / 82 / 74
1976 / 74 / 66 / 84 / 80
1977 / 74 / 74 / 84 / 78
1978 / 78 / 74 / 86 / 82
15 / Calculate the seasonal index number for each of the four quarters for following data.
Year / 1st Quarter / 2nd Quarter / 3rd Quarter / 4th Quarter
1980 / 106 / 124 / 104 / 90
1981 / 84 / 114 / 107 / 88
1982 / 90 / 112 / 101 / 85
1983 / 76 / 94 / 91 / 76
1984 / 80 / 104 / 95 / 83
1985 / 104 / 112 / 102 / 84
16 / Given the following quarterly sales figures in thousands of rupees for the years 1966-1969, find the specific seasonal by the method of moving averages.
Year / I / II / III / IV
1966 / 290 / 280 / 285 / 310
1967 / 320 / 305 / 310 / 330
1968 / 340 / 321 / 320 / 340
1969 / 370 / 360 / 362 / 380
17 / What is time series? Explain various components of time series.
18 / Explain/Write steps of Moving Average method with its merits and demerits.
19 / Explain/Write steps of Simple Average method.
20 / Explain/Write steps of ‘Ratio to moving Average’ Method.
21 / List Various Forecasting models. Explain any three of them.
22 / Explain Extrapolation model in forecasting.
23 / Explain Exponential smoothing model in forecasting.
Write algorithm for forward difference table.
Begin
For j=1 to (n-1) by 1 do
For i=1 to (n-j) by 1 do
If (j=1) then
Set dij = yi+1 – y i
else
Set dij = d(i+1)(j-1) – di (j-1)
Endif
Endfor
Endfor
End
Write algorithm for Backward difference table.
Begin
For j=1 to (n-1) by 1 do
For i=(j+1) to n by 1 do
If (j=1) then
Set dij = y i - yi+1
else
Set dij = di (j-1) - d(i+1)(j-1)
Endif
Endfor
Endfor
End
Write different methods of Interpolation.
Methods for equally spaced functions
- Newton’s forward interpolation formula
- Newton’s backward interpolation formula
- Gauss’s formula
- Stirling’s formula
- Bessel’s formula
- Laplace – Everett’s formula
Method for unequally spaced functions
- Lagrangian interpolation
- Newton’s divided difference interpolation formula
Define Extrapolation.
The process of estimating the value of independent variable y for a given value of x outside the range x1 ≤ x ≤x n is known as extrapolation.