Candidates are required to give their answer in their own words as far as practicable.
The figures in the margine indicate full marks.

Brief Answer Question

Attempt All question

10x2=20

Find the combined mean from the following data:

Group	A	B	C
Number	200	250	300
Mean	25	10	15

Coefficient of variation of a distribution is found to be 20% and variance of distribution is 36. Find the mean value of the distribution.

Find the Karl Pearson's Coefficient of Skewness, when mean = 45, mode = 48 and standard deviation = 15.

If P(A) = 0.6, P(B) = 0.56 and P(A∪B) = 0.75 find P(A∩B). Where A and B are not disjoint events.

The quartile deviation of a distribution is 2 and the difference between P9 and P10 is 8. Calculate the coefficient of Kurtosis.

Calculate coefficient of correlation between X and Y if the regression coefficient of Y on X is -0.667 and regression coefficient of X on Y is -0.75.

Find the simple aggregative price index number for the year 2021:

Commodities	A	B	C	D	E
Price in 2020	10	20	18	15	12
Price in 2021	15	22	20	22	18

What are the components of a time series.

Find the value of determinant:

1	5	6
2	3	7
3	5	6

10.

                        7   8            6   3
Find 7(A - B) where A = 9   10   and B = 3   2   
                        2    5           7   5

Group "B"

Descriptive Answer Question

Attempt any Five questions

5x10=50

11.

Calculate the Karl Pearson's Coefficient of Skewness and interpret the result.

Class	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Freq.	4	5	14	17	25	18	10	7

12.

Solve the following equations by using determinant or matrix method:
2x + 2y + z = 5
4x + 2y + 3z = 10
x + 3y + 4z = 7

13.

Following two groups of samples describes the age of the students in regular morning MBS program and evening MBS program of National College. If homogeneity of the class is a positive factor for learning which of the two programs will be easier to teach.

	24	30	28	23	25	22	26	27	28	25
Evening MBS	24	30	28	23	25	22	26	27	28	25
Morning MBS	28	27	34	33	29	27	28	29	33	26

14.

The following table gives the changes in the price and the consumption (quantity) of certain major constituents of the consumption basket of the labor class.

Commodity	Unit	2020		2021
		Price	Qty	Price	Qty
Wheat	Quintals	1000	10	1100	6
Rice	Quintals	1500	15	1700	18
Cloth	Meters	50	50	40	30

15.

(a) The probability that a boy will get a scholarship is 0.9 and that a girl will get is 0.8. What is the probability that at least one of them will get the scholarship? (b) The following table is the conditional payoff table:

Strategy	N₀(10)	N₁(11)	N₂(12)	N₃(13)	N₄(14)
S₁(10)	400	400	400	400	400
S₁(11)	380	440	440	440	440
S₁(12)	360	420	480	480	480
S₁(13)	340	400	460	520	520
S₁(14)	320	380	440	500	560

What will be your decision if: (i) Maximax criterion is used (ii) Maximin criterion is used (iii) Minimax regret criterion is used

16.

Solve the following Linear Programming problem graphically:
Maximize Z = 30x + 50y
Subject to constraints: x + y ≤ 30 x + 2y ≤ 40
and x ≥ 0, y ≥ 0

Group "C"

Analytical Answer Question

Attempt any Two questions

2x15=30

17.

Test for the normality of these two distributions of wages (in Rs.) and interpret the result on the basis of the information given below:

Daily wages in Rs.	No. of Workers X	No. of Workers Y
20 - 30	15	25
30 - 40	30	40
40 - 50	44	60
50 - 60	60	35
60 - 70	30	20
70 - 80	14	15
80 - 90	7	5

18.

Before and after the implementation of an economic program to uplift the economic condition of a community following information were found.

Monthly Income (in Rs. '00)	Prior to the plan No. of families	After the plan No. of families
4 - 6	10	65
6 - 8	70	-
8 - 10	35	37
10 - 12	20	15
12 - 14	10	15
14 - 16	3	5
16 - 18	2	5

a. Find the highest income of the poorest 40% of the population before and after the plan. b. Find the lowest income of richest 40% of the population before and after the plan. c. Obtain the limits of income of middle 50% of families before and after the plan.

19.

The income and expenditure of 100 families is given below:

Income (Rs)	Expenditure (Rs)
Income (Rs)	0 - 500	500 - 1000	1000 - 1500	1500- 2000
0 - 1000	-	-	-	3
1000 - 2000	-	4	9	4
2000 - 3000	3	10	19	8
3000 - 4000	7	6	12	5
4000 - 5000	9	7	-	-

Find (a) Two regression co-efficient.
(b) Co-efficient of correlation between income and expenditure.
(c) Estimate the expenditure when income is Rs 10,000.

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