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BBS Business Statistics

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BBS First Year Business Statistics Question Paper 2082 (TU) – Solved

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Faculty of Management

2082

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.

Calculate coefficient of variation of a distribution, when mean = 40 and standard deviation = 11.

[2]
2.

Find quartile coefficient of skewness, when median = 40, lower quartile = 33 and upper quartile = 45 .

[2]
3.

Twenty balls are numbered from 1 to 20. If one ball is drawn at random, what is the probability that the ball drawn is multiple of 4 or 7?

[2]
4.

Calculate the coefficient of kurtosis, when first quartile = 25, third quartile = 40, \( 10^{\text{th}} \)percentile = 10 and \( 90^{\text{th}} \) percentile = 63.

[2]
5.

Calculate regression coefficient of Y on X, if correlation coefficient between X and Y = 0.60, standard deviation Xseries = 7 and standard deviation of Y series = 9.

[2]
6.

Find the simple aggregative price index number for the year 2023 from the following information:

Commodities A B C D E
Price in 2022 15 25 23 25 17
Price in 2023 18 27 25 28 20

[2]
7.

List out the any four random sampling techniques.

[2]
8.

Find the value of following determinant:

\( \begin{vmatrix} 1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b \end{vmatrix} \)
[2]
9.

Find 3(A+B) where \( A = \begin{bmatrix} 1 & 9 \\ 4 & 1 \\ 3 & 7 \end{bmatrix} \) and \( B = \begin{bmatrix} 2 & 6 \\ 3 & 3 \\ 1 & 4 \end{bmatrix} \) . 

[2]
10.

From the given Pay-off table, give the decision according to (i) Maximax approach (ii) Maximin approach

State of nature Strategies
\( \text{S}_1 \) \( \text{S}_2 \) \( \text{S}_3 \)
\( \text{N}_1 \) 50 30 90
\( \text{N}_2 \) 70 80 40
\( \text{N}_3 \) 20 40 20

[2]

"Section B"

Attempt any FIVE questions .

[5*10=50]

1.

Find out the lowest marks of top 10 percent of the students from the following marks distribution: 

Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Students 4 5 14 17 25 18 10 7

[10]
2.

Solve the following equations by using determinant or matrix method:

2x - y + z = -2

x + y - 2z = -9

x + 2y + z = 9
[10]
3.

The following table gives the changes in price and quantity of the consumption basket of the labour class.

Commodity 2022 2023
Price Quantity Price Quantity
A 1200 10 1500 11
B 1700 12 1800 18
C 500 50 700 60
D 300 40 500 50

Calculate the cost of living index. If the average of a labour wage was Rs. 24,000 per month in 2022, what should be the average wage per worker per month in 2023, so that the standard of living of the workers does not falls in the year 2023 level?

[10]
4.

The following table shows the profit (Rs. millions) of a ABC company:

Year 2015 2016 2017 2018 2019 2020 2021 2022 2023
Profit 16 20 25 28 30 27 29 32 25

Fit a straight line trend by least square method. Calculate the trend values. Estimate the profit for the year 2024.

[10]
5.

Solve the following Linear Programing Problem graphically:

\( \text{Minimize } Z = 3x + 5y \)

\( \text{Subject to constraints: } x + 2y \ge 40 \)

\( x + y \ge 30 \)

\( \text{and } x \ge 0, y \ge 0 \)
[10]
6.

A vender buys magazine at the rate of Rs 10 and sells them at the rate of Rs 15. The unsold magazines will be worthless. The number of copies demanded and their corresponding probabilities are given below:

Copies demanded Probability
200 0.19
210 0.16
220 0.25
230 0.27
240 0.13

(a) Determine optimum stock level (b) Calculate maximum expected monetary value (EMV).

[10]

"Section C"

Attempt any TWO Questions .

[2*15=30 ]

1.

The following table revels daily wages (Rs.00) of workers of certain locality:

Daily wages (Rs.00) Number of workers
20 – 30 10
30 – 40 15
40 – 50 21
50 – 60 30
60 – 70 24
70 – 80 15
80 – 90 5

Calculate (a) coefficient skewness and interpret the result (b) coefficient of kurtosis and interpret the result.

[15]
2.

The following table shows the income and expenditure of people:

Income (Rs 000) Expenditure (Rs.000)
100 80
80 60
50 30
40 35
70 40
60 50
90 55
75 40
95 50
30 20

a. Calculate Karl Preason's correlation coefficient.

 b. Find out two regression coefficients.

 c. Estimate the expenditure a person when his/her income is Rs 85 thousand.

[15]
3.

Following samples describes the marks of the students in Statistics in BBS program of two sections.

Section A 54 60 58 53 55 52 56 57 58 55
Section B 58 57 54 53 59 57 58 59 63 56

(a) State which section of students securing more uniform marks?

(b) Find out combined standard deviation.

[15]