BUSINESS STATISTICS COMPLETE NOTES FOR UPCOMING EXAM
STATISTICS INTRODUCTION
DIAGRAMS AND GRAPHS
MEASURE OF CENTRAL TENDENCY AND DISPERSION
CORRELATION AND REGRESSION ANALYSIS NOTES
INDEX NUMBER NOTES
TIMES SERIES ANALYSIS NOTES
BUSINESS FORECASTING NOTES
STATISTICS INTRODUCTION
DIAGRAMS AND GRAPHS
MEASURE OF CENTRAL TENDENCY AND DISPERSION
CORRELATION AND REGRESSION ANALYSIS NOTES
INDEX NUMBER NOTES
TIMES SERIES ANALYSIS NOTES
BUSINESS FORECASTING NOTES
BUSINESS STATISTICS QUESTION BANK FOR NOVEMBER’ 2019 EXAM
Unit 1 – Measures of Central tendency and Dispersion
Theoretical Questions:
Q. Define statistics. What are its characteristics? Mention its importance and limitations.
Q. What are various types of statistical data? Distinguish between primary and secondary data. Mention various methods for collecting data.
Q. What is census and sample survey? Distinguish between them. What are their merits and demerits?
Q. What are the essential qualities of a measure of central tendency and a good measure of dispersion?
Q. What is dispersion? What purpose does it serve? What are its various types? Distinguish between absolute and relative measures of dispersion.
Q. Prove that:
- AM > GM > HM
- GM = nth root of product of AM and HM
Practical Problems:
1. If A.M. and G.M. of two numbers are 4 and 4 respectively, find their H.M. and those two numbers.
2. Prove that – 
3. If 
prove that 
(a and b are constant.)
prove that (a and b are constant.)
4. If a constant 2 is added to each observation of series, prove that AM is increased by 2.
5. Fill up the gaps:
(i) H.M. of 3 and 4 is ____.
(ii) 
(iii) 
(iv) 
is called. ____.
is called. ____.
6. Find median of 8, 6, 11, 14, 10 and 16.
7. Prove that 
8. If 
and 
, find 
and , find
9. Write down one use of each of G.M. and H.M.
10. Prove that : 
11. If 
median = 27.5, find mode.
median = 27.5, find mode.
12. ____ is called average of position. (Fill in the blank)
13. If any value of set of observations is zero, then ____ of the observation will be zero. (Fill in the blank)
14. Which measure of central tendencies may be of more than one value?
15. The point where the two ogives intersect is the ____ of the distribution. (Fill in the blanks)
16. What is geometric mean of 4, 10 and 25?
17. The algebraic sum of deviations of the observations from their arithmetic mean is ____.
18. The geometric mean of n observations is G. If each observations is multiplied by 3, then what will be the new geometric mean?
19. If AM of 
is 
, then AM of 
is ____. (Fill in the blank)
is , then AM of is ____. (Fill in the blank)
20. Arithmetic mean of samples of sizes 50 and 75 and 60 and x respectively. If the arithmetic mean of 125 observations of both the samples taken together be 54, find x.
21. Which of the following is affected by extreme values? (i) Arithmetic mean. (ii) Median. (iii) Mode.
22. Find the weighted AM of 1, 2, 3, 4 with corresponding weights 4, 3, 2,and 1 respectively.
23. What type of average should be used in the following cases? (i) Size of ready-made shirts in a shop. (ii) Estimation of intelligence of students in a class. (iii) To find the average speed when time of journey is given.
24. If a constant 2 is added to each observation of series, prove that AM is increased by 2.
25. Calculate Mean, Median, Mode, Q1, Q3, D9 and P60 from the below mentioned data:
a) 4, 4, 3, 3, 4, 5, 7, 8, 7, 8, 15, 20, 10, 3.
b) 1, 2, 3, 4, 5, 6
26. Find the weighted AM of 1, 2, 3, and 4 with corresponding weights 4, 3, 2, and 1 respectively.
27. Calculate Mean, Median, Mode, Q1, Q3, D9 and P60 from the following data:
X
|
10
|
20
|
30
|
40
|
50
|
F
|
5
|
6
|
10
|
5
|
4
|
28. Find mean Median, Mode, D8, Q3 and P64.
Class :
|
0 – 99
|
100 – 199
|
200 – 299
|
300 – 399
|
400 – 499
|
500 – 599
|
Frequency :
|
3
|
10
|
36
|
42
|
6
|
3
|
29. Find Mean, Median, Mode, D5, Q1 and P40
Marks (above) :
|
10
|
20
|
30
|
40
|
50
|
No. of Students:
|
59
|
54
|
46
|
34
|
18
|
30. Find Mean, Median, Mode, D5, Q1 and P40
Class :
|
15 – 25
|
25 – 35
|
35 – 45
|
45 – 55
|
55 – 65
|
65 – 75
|
Frequency :
|
4
|
11
|
19
|
14
|
0
|
2
|
31. Find Mean, Median, Mode, D5, Q1 and P40
Marks
|
Below 10
|
10 – 20
|
20 – 30
|
30 – 40
|
40 – 50
|
50 – 60
|
60 - 70
|
Above 70
|
No. of Students :
|
5
|
25
|
40
|
70
|
90
|
40
|
20
|
10
|
32. If the AM of the following distribution is 124, find the value of x.
Weight :
|
110
|
120
|
135
|
X + 5
|
No. of Persons :
|
3
|
3
|
2
|
2
|
33. Find mean, median and mode of the following data:
Mid value of classes:
|
100
|
110
|
120
|
130
|
Frequency:
|
20
|
26
|
38
|
16
|
34. Median of the following distribution is 24.2, find f2. Also find mean and mode.
Class :
|
10 – 14
|
15 – 19
|
20 – 24
|
25 – 29
|
30 – 34
|
35 – 39
|
Frequency :
|
5
|
f2
|
4
|
8
|
4
|
3
|
35. A car covers four sides of a square at speed 5, 10, 20 and 25 km/hr. respectively. What is the average speed of the car around the square?
36. A man travelled 20 km at 5km/h and again 24 km at 4 km/h. Find the average speed of the man.
37. The arithmetic mean of the marks secured by two groups of students are respectively 70 and 80. If the AM of the marks secured by all the students is 74, find the ratio of number of students of the3 two groups.
38. The average marks secured by boys and girls in a class are respectively 45 and 55, and the average marks secured by all of them is 48. Find the P.C. of boys and girls in the class.
39. Arithmetic mean of samples of sizes 50 and 75 and 60 and x respectively. If the arithmetic mean of 125 observations of both the samples taken together be 54, find x.
40. From the following data, find and if AM of the following distribution is 72.5 marks:
Marks:
|
No. of Students
|
30 – 39
40 – 49
50 – 59
60 – 69
70 – 79
80 – 89
90 – 99
|
2
3
11
F1
32
F2
7
N = 100
|
41. From the following data, find and if Median of the following distribution is 72.5 marks:
Marks:
|
No. of Students
|
30 – 39
40 – 49
50 – 59
60 – 69
70 – 79
80 – 89
90 – 99
|
2
3
11
F1
32
F2
7
N = 100
|
42. From the following data, find and if Mode of the following distribution is 72.5 marks:
Marks:
|
No. of Students
|
30 – 39
40 – 49
50 – 59
60 – 69
70 – 79
80 – 89
90 – 99
|
2
3
11
F1
32
F2
7
N = 100
|
Measure of Dispersion
Q. Find Range, QD, MD and SD from the following data: 1, 3, 5, 7, 9
Q. If S.D of x is 5, find S.D. of: (i) 2x – 3 (ii) 2x + 5 (iii) x/5 + 1
Q. Given 
, 
and 
, find 
[H.S.’ 99]
, and , find [H.S.’ 99]
Q. Fill up the gaps: (i) S.D. of 3 and 4 is ____. (ii) 
is called ____.
is called ____.
Q. If 
, 
and 
, find 
, and , find
Q. What purpose do dispersion serve? Give two examples.
Q. If S.D of x is 5, find S.D. of: (i) 
and (ii) 
and (ii)
Q. If 
and 
are the standard deviations of series I and series II respectively, find the relations between and 
:
and are the standard deviations of series I and series II respectively, find the relations between and :
Series I :
|
5
|
7
|
12
|
17
|
20
|
Series II :
|
17
|
23
|
38
|
53
|
62
|
Q. Find the co-efficient of variation of the following numbers: 1, 2, 3, 4, 5
Q. Find Standard Deviation: 
, 
, 
, ,
Q. 
is S, then SD of 
.
is S, then SD of .
Q. Standard deviation of 7 and 3 is ____. (Fill in the blank)
Q. SD of 1, 2, 3, 4, 5 is
Q. If 
, 
, 
find the coefficient of variation.
, , find the coefficient of variation.
Q. If SD of 
be 
, what will be SD of 
?
be , what will be SD of ?
Q. If 
, 
, 
, then find the value of r.
, , , then find the value of r.
Q. If the mean deviation for a group of 50 items is 16.2, what will be their SD?
Q. AM and SD of a set of values are 30 and 8 respectively. If 2 is added to each value, then what will be the coefficient of variation of the series? Find it.
Q. If AM of 
, then find 
.
, then find .
Q. SD of 7, 7, 7, 19, 19, 19 is ____.
Q. Coefficient of variation is expressed in ____.
Q. AM and SD of a set of values are 30 and 8 respectively. If 2 is added to each value, then what will be the coefficient of variation of the series? Find it.
Q. If S.d. of 2,5,6,8,9,is 2.449, then find the sd of (i) 15,18,19,21,22 (ii) 4,10,12,16,18 (iii) 5,11,16,17,19.
Q. From the following data, find Range, QD, MD about Mean and Median, standard deviation and CV.
X:
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
Y:
|
2
|
7
|
11
|
15
|
10
|
4
|
1
|
Q. Find MD, QD and Standard deviation:
Class :
|
500 – 599
|
600 – 699
|
700 – 799
|
800 – 899
|
900 – 999
|
1000 – 1099
|
Frequency :
|
5
|
17
|
27
|
41
|
6
|
4
|
Q. Find the mean, S.D., coefficient of sd and coefficient of variation:
Age
|
20 – 25
|
25 – 30
|
30 – 35
|
35 – 40
|
40 – 45
|
45 – 50
|
50 – 55
|
55 – 60
|
No. of Persons
|
50
|
70
|
100
|
180
|
150
|
120
|
70
|
60
|
Q. Find the sd and variance of the following data:
Marks less than :
|
10
|
20
|
30
|
40
|
50
|
60
|
No. of Students :
|
6
|
10
|
16
|
28
|
30
|
40
|
Q. The mean and S.D of 100 numbers are found to be 30 and 10 respectively. Two numbers were taken by misstate as 12 and 31 instead of 21 and 13 respectively. Find the correct mean and S.D.
Q. From a certain frequency distribution consisting of 20 observations the mean and SD were found to be 10 and 2 respectively. At the time of checking it was found that a figure 12 was miscopied at 8. Calculate the correct mean, SD and Coefficient of variation if wrong item is replaced.
Q. Mean and S.D. of 18 observations are found to be 7 and 4 respectively. But on comparing the original data it was found that on observation 12 was miscopied as 21 in the calculation. Calculate correct mean and S.D. if wrong item is omitted.
Q. Find the M.D. from the mean of the following data :
Class :
|
0 – 5
|
5 – 10
|
10 – 15
|
15 – 20
|
20 – 25
|
25 – 30
|
30 – 35
|
Frequency :
|
2
|
7
|
10
|
12
|
9
|
6
|
4
|
Q. Find the Q.D. and variance of the data of the following distribution:
Mid value of classes:
|
100
|
110
|
120
|
130
|
Frequency :
|
20
|
26
|
38
|
16
|
Q. From the following data, find co-efficient of variation : A = 10, Sum of D2 = 10, N = 5, Mean = 8.
Q. Following are the heights (in cm) of 11 students: 124, 127, 126, 123, 127, 129, 125, 130, 132, 130, 121. Calculate the quartile deviation.
Q. The weekly wages of workers in two factories show the following results :
Factory –A
|
Factory –B
| |
Mean Wages :
Standard Deviation of Wages :
|
500
28
|
425
35
|
a) In which factory is there greater variation in the distribution of wages?
b) Which factory is paying highest amount of wages?
Q. Fill in the blanks: If AM and SD of a series are respectively 80 and 16, then the coefficient of variation would be ____ which means that the SD is ____% of the mean. If coefficient of variation of the series A is greater than that of the series B, then series A is ____ uniform than the series B.
Q. The mean of five observations is 4.4 and variance is 8.24. If three of observations are 4, 6 and 9, then find the other two.
Q. Calculate Range, SD, QD, MD about mean and MD about median and their relative measures from the following data:
Class Interval:
|
0 – 10
|
10 – 20
|
20 – 30
|
30 – 40
|
40 – 50
|
Frequency:
|
4
|
5
|
6
|
3
|
1
|
Q. Calculate Range, SD, QD, MD about mean and MD about median and their relative measures from the following data:
Class Interval:
|
0 – 9
|
10 – 19
|
20 – 29
|
30 – 39
|
40 – 49
|
Frequency:
|
4
|
5
|
6
|
3
|
1
|
Q. Calculate Range, SD, QD, MD about mean and MD about median and their relative measures from the following data:
Class Interval:
|
0 – 10
|
0 – 20
|
0 – 30
|
0 – 40
|
0 – 50
|
Frequency:
|
4
|
9
|
15
|
18
|
19
|
Q. Calculate Range, SD, QD, MD about mean and MD about median and their relative measures from the following data:
Class Interval:
|
0 – 50
|
10 – 50
|
20 – 50
|
30 – 50
|
40 – 50
|
Frequency:
|
19
|
15
|
10
|
4
|
1
|
Q. Mr. A wants to invest Rs. 10,000 in one of the two companies A or B. Average return in A is Rs. 16000 with SD of Rs. 125 and average return of B is Rs. 20,000 with Sd of Rs. 200. Suggest which company is to be selected.
Unit 2 – Correlation and Regression analysis
Theoretical Questions:
Q. What is correlation analysis? What are its various kinds? What is its range?
Q. Define regression analysis. Why there are two regression lines? Distinguish between correlation and regression.
Q. What are the uses and limitations of correlation and regression analysis?
Q. Write the properties of coefficient of correlation. Prove that:
- Correlation coefficient is the geometric mean of two regression coefficient
- Correlation coefficient is independent of the change of the origin and scale of measurement
- Regression coefficient is independent of the change of the origin and but dependent on scale of measurement
Q. Mention three methods for calculation of coefficient of correlation.
Practical Problems:
Q. From the following data obtain the following:
1. Correlation Coefficient using 5 methods (Actual mean, assumed mean, direct method, covariance method and product moment formula) of Karl Pearson
2. Obtain two regression lines
3. What will the value of x if y = 15 and what will the value of y if x = 20
X:
|
6
|
2
|
10
|
4
|
8
|
Y:
|
9
|
11
|
5
|
8
|
7
|
Q. Calculate Rank correlation from the data given below:
X:
|
39
|
62
|
62
|
90
|
82
|
75
|
75
|
98
|
36
|
78
|
Y:
|
47
|
53
|
58
|
58
|
62
|
68
|
60
|
91
|
51
|
84
|
Q. Calculate Rank correlation:
Rank 1
|
2
|
3
|
4
|
5
|
1
|
9
|
7
|
8
|
4
|
Rank 2
|
1
|
3
|
5
|
2
|
4
|
6
|
9
|
7
|
8
|
Q. Calculate the correlation coefficient by Pearson’s formula of the following data:
X
|
6
|
2
|
10
|
4
|
8
|
Y
|
9
|
11
|
?
|
8
|
7
|
Given, Mean for X = 6, Mean for Y=8.
Q. Pearson’s coefficient of correlation of two variates X and Y is 0.28, their covariance is + 7.6. If the variance of X is 9, then find the s.d. of Y- series.
Q. Find the correlation coefficient from the following data: Sum of X = 56, Sum of Y = 40, Sum of X2 = 524, Sum of Y2 = 256, Sum of Product of XY = 364, n = 8.
Also find two regression equations. If the value of X is 30 then find the value of Y and again if the value of Y is 50 then find the value of X.
Q. A computer while calculating the correlation coefficient between two variable X and Y obtained the following results: Sum of X = 56, Sum of Y = 40, Sum of X2 = 524, Sum of Y2 = 256, Sum of Product of XY = 364, n = 8. It was, however, later discovered that two pairs of observations (6,4) and (3,5) were taken wrongly instead of correct values (4,6) and (7,1) respectively. Calculate the correct value of correlation co-efficient between X and Y.
Q. Find Pearson’s co-efficient of correlation from the following data: N=10, Sum of X =140, Sum of Y = 150, Sum of (X – 10)2=180, Sum of (Y – 15)2= 215, Sum of (X – 10)(Y – 15)=60.
Q. The demand of TV sets as obtained by a sample survey on the residents of 7 towns is shown below :
Population (in’ 000):
|
11
|
14
|
14
|
17
|
17
|
21
|
25
|
Demand of TV:
|
15
|
27
|
27
|
30
|
34
|
38
|
46
|
Find the linear regression equation of Y on X and also find the demand of TV sets in a town of population 30 thousand
Q. Given the two regression equation as 8x – 10y + 66 = 0 and 40x – 18y =214? Do you agree with the given equations? If yes then state which equation is of X on Y and Y on X find:
a) The coefficient of correlation between x and y.
b) Mean for X and Y.
c) SD of X if variance of Y is 100.
Q. Find out the value of Y when X = 36 from the data given below:
X
|
Y
| |
Mean
Standard Deviation
|
30
4
|
45
10
|
Correlation coefficient = +0.8
| ||
Q. Find the two regression equations from the data given below: N=10, Mean for X = 4, Mean for Y = 2, Sum of XY = 480, Sum of X2 =1680, Sum of Y2=320
Unit 3 – Index Number
Theoretical Questions:
Q. Explain index number. Mention its importance (Uses) and Limitations. What are the problems in construction in index number?
Q. Mention three types of index number. (Price Index number, quantity index number and value index number)
Q. Mention two merits and demerits of Laspeyre’s and Paasche’s index number.
Q. Why Index number is called “Economic Barometer” (Uses of Index number)?
Q. Distinguish between:
(a) Time reversal test and Factor reversal test
(b) Price index and Quantity index number
(c) Weighted and Unweighted (Simple) Index number
(d) Fixed base and chain base index number
Q. What is cost of living index? What is its importance?
Q. Mention any three important methods for calculating index number. Why fisher’s index is called ideal index number?
Practical Problems:
Q. Find the simple aggregative index number and simple average of price relatives (AM) for the data given below:
Commodity
|
A
|
B
|
C
|
D
|
E
|
Base Price
Current Price
|
40
50
|
22
25
|
31
29
|
10
12
|
75
100
|
Q. Find simple index number, Fixed base index number and chain base index number:
Year
|
1980
|
1981
|
1982
|
1983
|
1984
|
Price of Rice
|
10
|
11
|
12
|
13
|
14
|
Q. Index number of various years is given below taking 1980 as base. Shift the base to 1982
Year
|
1980
|
1981
|
1982
|
1983
|
1984
|
Index Number
|
100
|
110
|
120
|
130
|
140
|
Q. Find the index number by using (i) Unweighted (ii) Weighted aggregative method (AM Method) from the following data:
Commodities
|
Base Price (2005)
|
Current Price (2010)
|
Weight
|
Rice
Dal
Fish
Potato
Oil
|
36
30
130
40
100
|
54
50
155
35
110
|
10
3
2
4
5
|
Q. From the given data calculate the following:
Commodity
|
1990
|
1993
| ||
Price
|
Quantity
|
Price
|
Quantity
| |
A
B
C
D
|
6
2
4
10
|
50
100
60
3
|
10
2
6
12
|
56
120
60
24
|
1. Laspeyre’s Price Index and Laspeyre’s Quantity Index
2. Paasche’s Price index and Paasche’s Quantity index
3. Fisher’s price index and Fisher’s Quantity index
4. Marshall - Edgeworth Price index and Marshall - Edgeworth Quantity index
5. Time reversal test and factor reversal test of Fisher’s index number
6. Value index number
Q. Calculate CLI (Weighted) and unweighted index number:
Expenditure
|
Food
|
Rent
|
Clothes
|
Petrol
|
Medicine
|
Others
|
% of Exp.
Prices in 1975
Prices in 1976
|
35%
50
40
|
10%
40
40
|
20%
30
40
|
15%
30
35
|
15%
10
20
|
5%
10
15
|
Mr. X used to get Rs.240 in 1975 and in 1976 he gets Rs. 250. To maintain the same standard of living at present how much dearness allowance should he get (If any)?
Q. Construct the general index number from the following data:
Group
|
A
|
B
|
C
|
D
|
E
|
Group Index
Weight
|
152
48
|
110
5
|
130
10
|
100
12
|
80
15
|
Q. In constructing CLI the following weights were used: Food 15, Rent 4, Garments 3, Fuel & light 2 and misc. 1. Calculate the index number for a data when the percentage increase in price of the various items over prices of july 2005 (=100) were 32, 47, 54, 78 and 58 respectively. By the same period wages of a worker was also increased from Rs. 325 to Rs. 500? Was there may any gain or loss for that worker? If so find by how much?
Q. In a working-class consumer price index number of a particular town the weights corresponding to different groups of items were as follows: food 45, rent 15, garments 12, fuel & light 8 and misc. 20. On the basis of base year indices of current year are respectively 410, 150, 343, 248 and 285. Find the CLI of current year. Mr. X used to get Rs.24000 in base year and in current year he gets Rs. 43000. To maintain the same standard of living at present how much dearness allowances should we get?
Q. The table give the average wages in Rs. Per day of a group of workers from 1947 to 1951 and consumer price index for these years. Determine the real wages of the workers:
Year
|
1999
|
2000
|
2001
|
2002
|
2003
|
Average Wages
|
1.19
|
1.33
|
1.44
|
1.57
|
1.75
|
Consumer index number
|
95.5
|
102.8
|
101.8
|
102.8
|
111.0
|
Q. The following are the two sets:
(A) Year:
|
1971
|
1972
|
1973
|
1974
|
1975
|
Index Number (Base Year = 1971)
|
100
|
108
|
112
|
120
|
160
|
(B) Year:
|
1975
|
1976
|
1977
|
1978
|
1979
|
Index Number (Base Year = 1975)
|
100
|
120
|
110
|
130
|
140
|
Slice (i) the series B to A shifting the base of series B to 1971 and (ii) the series A to B shifting the base of A to 1975.
Unit 4 – Time Series analysis
Theoretical Questions:
Q. What is time series analysis? Mention its utilities.
Q. Discuss the components of time series analysis. Mention the two models used for time series analysis.
Q. What is Trend or secular trend? Mention the factors responsible for trend.
Q. Discuss various methods used for time series analysis.
Q. Explain least square method of time series analysis with respective merits and demerits.
Q. Write short notes on shifting of trend and deseasonalised value.
Practical Problems:
Q. Obtain trend values for from the following data by following the below mentioned methods:
Year
|
1971
|
1972
|
1973
|
1974
|
1975
|
1976
|
Values
|
51
|
53
|
58
|
60
|
62
|
67
|
1. Semi Average Method
2. 3 Yearly moving average method
3. 3 yearly weighted moving average with weight of 1,2,1.
Q. Obtain trend values for from the following data by following the below mentioned methods:
Year
|
1971
|
1972
|
1973
|
1974
|
1975
|
1976
|
1977
|
1978
|
Values
|
51
|
53
|
58
|
60
|
62
|
67
|
42
|
43
|
- Semi Average Method
- 4 Yearly moving average method
- 4 yearly weighted moving average with weight of 1,2,1,1.
Q. find the moving average of order 3 from 2,6,1,5,7,3,2.
Q. Using the least square principle and parabolic trend find the trend values from the following data:
Year:
|
1990
|
1991
|
1992
|
1993
|
1994
|
1995
|
1996
|
Production:
|
83
|
60
|
54
|
21
|
22
|
13
|
23
|
Q. Calculate trend values for the year 2007 and 2010 by using the method of least squares from the data given below:
Year :
|
2001
|
2002
|
2003
|
2004
|
2005
|
2006
|
Values :
|
101
|
107
|
113
|
121
|
136
|
148
|
Also fit an equation of the type = a+bt+ct2 to the given data.
Q. Using the method of least squares, find the trend values for the following data:
Year
|
1985
|
1990
|
1995
|
2000
|
2005
|
2010
|
2015
|
Income
|
67
|
53
|
43
|
61
|
56
|
79
|
58
|
Also find:
- The estimated income for 2020.
- Find the slope and intercept of the straight line trend.
- Do the figures show a rising trend or a falling trend.
- What does the difference between the given figures and trend values indicate?
Q. Find the quarterly trend values from the following data by:
- Moving average method using an appropriate period
- Ratio to moving average
- Seasonal variations using moving average method
- Seasonal indices
- Seasonal movement
Quarter/Year
|
1964
|
1965
|
1966
|
I
II
III
IV
|
52
54
67
55
|
59
63
75
60
|
57
61
72
50
|
Q. The trend equation for publicity cost (Rs. In’ 000) of a company is YC=20.2 – 0.8t. Origin 2001 (1st July), t unit = 1 year, Y unit = yearly cost. Shift the origin to 2010.
Q. The equation for yearly sales for a commodity with 1st july 1971 as origin is Y = 81.6 + 28.8X. Determine the trend equation to give monthly trend values with 15th jan 1972 as origin.
Q. The Parabolic trend equation for the sales (in ‘000 Rs.) of a company is given as: Y = 14.1 – 0.80x + 0.5x2. origin = 1984 (1st july); unit = 1 year; y = yearly sales. Shift the origin to 1988.
Q. On the basis of quarterly sales of a certain commodity for the period 1961 – 63, the following results were computed: Trend values: Y = 27.2 + 0.6 t, with origin 1st quarter 1961, t = time units and y = quarterly sales. The seasonal index are 1st qtr” 90, 2nd qtr = 95, 3rd qtr = 110 and 4th qtr = 105. Estimate the quarterly sales for the year 1963.
Q. Deseasonalise the following data using a multiplicative model:
Quarter:
|
1
|
2
|
3
|
4
|
Sales:
|
65.4
|
25.2
|
23.7
|
21.4
|
Seasonal Index:
|
148
|
124
|
78
|
59
|
Unit 5 – Business forecasting (Old Course)
Q.What is business forecasting? Explain its purpose or objectives.
Q. What are the assumptions of business forecasting? Explain any three methods of forecasting.
Q. What are advantages and limitations of business forecasting? Mention the steps involved in business forecasting.
Q. Distinguish between Demand forecasting and Sales forecasting. What are the steps involved in demand forecasting?
Q. Explain any three theories of business forecasting.
Multiple Choice Questions for November’ 2017:
Unit – 1: Average and Dispersion
Q. Calculation of GM, HM, AM from 5,3,3,1,3,3,4,1,0
Q. Define sample and census.
Q. Define pie chart and bar diagram.
Q. What is frequency distribution table?
Q. Which is best measure of dispersion (SD) and best measure of central tendency (Mean)?
Q. Range = H – L
Q. Q2 = 1/2(Q1 + Q3)
Q. SD of two given numbers = 1/2 (H – L)
Q. SD of natural number = square root of (n2- 1)/12
Q. If SD of X is 5 then SD of 2x – 1 and 4x/2 + 1 will be: 10 in each case.
Unit – 2: Correlation and Regression
Q. Range of correlation = +1 to -1.
Q. Increase on prices and selling of products = Negative correlation
Q. Age of husbands and wives = Positive correlation
Q. Intelligence and size of shoe = No correlation
Q. Karl Pearson’s coefficient of correlation measures QUANTITATIVE DATA.
Q. Spearmen’s Rank correlation measures QUALITATIVE DATA.
Q. r is the GM of two regression coefficients.
Q. There is only one line if r = + 1.
Q. Regression lines will be parallel if r = 0.
Q. No of regression lines: 2
Q. Two regression lines intersect at the respective mean of X and Y.
Unit – 3: Index Number
1. Only Fisher’s index number is the ideal index number which satisfied time reversal and factor reversal test.
2. Fisher’s index is the GM of Laspeyre’s and Paasche’s index number.
3. Base year index = 100
4. P01 x P10 = 1 or P0n x Pn0 = 1
5. P01 x Q01 = Value index number
6. Net monthly income of an employee was Rs.800 pm in 1980. The consumer price index number was 160 in 1980. It rises to 200 in 1984. Calculate DA and his wages.
Ans: DA = 40/160*800 = 200 and his wages should be = 200/160*800 = 1000
7. Index number in 2000 is 140 which increase to 200 in 2010. What does it mean?
Ans: It means prices are increased by 60% in 2010 as compared to 2000.
Unit – 4: Time Series Analysis
Q. Examples of irregular variation: Flood, fire, strike, lockout, earthquake, hot wave in winter, rain in desert.
Q. Examples of seasonal variation: sale of woolen clothes during winter, decline in ice-cream sales during winter, demand of TV during international games.
Q. Examples of cyclical variation: Recession, Boom, Depression, Recovery, balancing of demand and supply.
Q. Examples of Trend or secular trend: Increase in demand of two wheeler, decrease on death rate due to advancement of medical science, increase in food production due to increase in population.
Q. Multiplicative model: T.C.S.I and Additive model: T + C + S + I. here T = Secular Trend, C = Cyclical trend, S = Seasonal variation and I = Irregular variation.
Q. Short term forecasting = Seasonal trend and long term forecasting = Secular trend.
Q. Y = TCSI (Multiplicative model) or T + C + S + I (Additive model).