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BBS Business Statistics

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BBS First Year Business Statistics Question Paper 2083 (TU) – Solved

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Faculty of Management

2083

Bachelor of Business Studies

Business Statistics

MGT 202

Full Marks: 100

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

"Section A"

Attempt All questions .

[10*2=20 ]

1.

Mean of 100 items was 50. Later on it was found that two items were misread as 92 and 8 instead of 192 and 88. Find the correct mean.

[2]
2.

If \( \text{mean} = 45 \),\( \text{standard deviation} = 10 \)and \( \text{mode} = 43.7 \). Find Pearson's coefficient of skewness.

[2]
3.

Frequency distribution has Karl Pearson's coefficient of skewness is 0.5, mean is 5 and standard deviation is 2. Find the mode of the distribution.

[2]
4.

If \( A = \begin{bmatrix} 1 & 4 \\ 3 & 2 \\ 2 & 5 \end{bmatrix}, B = \begin{bmatrix} -1 & -2 \\ 0 & 5 \\ 3 & 1 \end{bmatrix} \). Find (A+B)

[2]
5.

If regression coefficient of y on \( x (b_{yx}) = -0.61 \) and regression coefficient \( x on y (b_{xy}) = -0.53 \), calculate the coefficient of correlation and interpret the result.

[2]
6.

The standard deviation of symmetrical distribution is 5. What must be the value of fourth moment about mean in order that the distribution be mesokurtic?

[2]
7.

A bag contains 20 balls numbered from 1 to 20. One ball is drawn at random. Find the probability that the number of the drawn ball be multiple of 3 or 7.

[2]
8.

Find the value of determinant of following matrix: \( \begin{bmatrix} 1 & 2 & 3 \\ 2 & 5 & 1 \\ 9 & 3 & 2 \end{bmatrix} \)

[2]
9.

The trend line equation of sales (in millions rupees) is Y = 50 + 2.5X. Estimate the sales for the year 2022, when year of origin is assumed to be 2015.

[2]
10.

List different sources of secondary data.

[2]

"Section B"

Attempt any FIVE questions .

[5*10=50 ]

1.

The following table represents the marks of 100 students : 

Marks 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100
No. of students 14 - 27 - 15

If the median mark is 48, find the missing frequencies.

[10]
2.

Calculate the Karl Pearson's coefficient of skewness.

Value 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25
Frequency 11 14 30 12 3

[10]
3.

Fit a straight line trend by the method of least squares and estimate the sales for 2004 and 2005.

Years 1998 1999 2000 2001 2002 2003
Sales (in '000Rs) 40 52 54 52 50 53

[10]
4.

Solve the equations by matrix or determinant method:

\( x_1 + 3x_2 + 4x_3 = 7 \)
\( 4x_1 + 2x_2 + 3x_3 = 10 \)
\( 2x_1 + 2x_2 + 2x_3 = 6 \)
[10]
5.

(a) A box contains 4 black and 4 red balls. If 2 balls are drawn at random find the probability that both are black.

(b) From the given payoff table, give decision according to minimax regret criteria:

Payoff Matrix

Courses of actions State of nature (events) - Demand
\( S_1 - 100 \) 500 500 500
\( S_2 - 100 \) 300 550 550
\( S_3 - 100 \) 100 350 600

[10]
6.

Solve the following linear programming problem graphically:

\( \text{Maximize } Z = 40A + 70B \)
\( 3A + 3B \le 36 \)
\( 5A + 2B \le 50 \)
\( 2A + 6B \le 60 \)
\( \text{\& } A, B \ge 0 \)
[10]

"Section C"

Attempt any Two Questions .

[2*15=30]

1.

The profit distribution of two companies A and B are given below:

Profit (million Rs.) 0 - 2 2 - 4 4 - 6 6 - 8 8 - 10 10 - 12
No. of Item A 2 7 11 20 7 3
No. of Item B 5 4 9 13 15 4

a) An investor wants to invest according to the profit of the company, which company shows more consistent on the basis of profit.

b) Also find the combined standard deviation.

[15]
2.

Calculate the price index number of a group of four commodities by using (a) Laspeyre's formula (b) Fisher's formula and (c) Paasche's formula:

Base year Current year
Commodity Price/unit Expenditure price/ unite Expenditure
A 2 40 5 75
B 4 16 8 40
C 1 10 2 24
C 5 25 10 60

Also, examine time reversal test and factor reversal test are satisfied on Fisher's index number.

[15]
3.

The following data shows the income and expenditure of employees of a factory:

Income (Rs 000) Expenditure ( Rs.000)
25 20
27 21
30 25
32 27
35 30
40 30
42 32

a. Calculate coefficient of correlation between income and expenditure.

b. Find out two regression coefficients.

c. Estimate the expenditure when income = Rs. 45 thousand.

[15]