Business Statistics (Quantitative Techniques): Notes, Questions

Business Statistics: Key concepts, questions, and assignments. Quantitative Techniques in in business decision making.

Management (MBA) questions, assignments on Business Statistics on Business Statistics.

Q. For the given data set representing the runs scored by two players in last 15 matches, conduct the following analysis:

Data:
Match No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Player A 8 42 56 68 91 123 12 46 57 137 5 80 14 10 19
Player B 38 44 46 59 57 61 48 42 51 39 58 41 55 45 68

i. Which average you will use to summarize the performance of the player? Find average runs scored for both of the players. Also give reasons for the choice of the average?
ii. If selection is possible on the basis of consistency, which player would you choose in the team? Perform the required statistics and justify the selection.
iii. Check whether there exists any relationship among the runs scored by two players using Karl Pearson coefficient of correlation and interpret the same.

Q. On the basis of the following data, the marketing manager wants to predict the sales volume for the locality on the basis of # households, number of cars and marketing expense:

Data:
Sl.No. Sales Volume #Households number of cars marketing expense
1 15727 161 3 180
2 9328 99 1 150
3 13681 135 2 175
4 12379 120 2 165
5 15351 164 3 178
6 24174 221 5 220
7 20154 179 4 205
8 20671 204 5 210
9 22978 214 5 128
10 13522 101 1 176
11 22471 231 5 226
12 19529 206 4 296
13 24216 248 3 240
14 11521 107 2 168
15 197.82 205 3 100

i. Draw three scatter plots of sales volume with each of the three variables and comment on their correlation.
ii. Regress the sales volume on #household, number of cars and marketing expense. Calculate R square and interpret the same.
iii. Determine which variable is/are significant variable/s. Is there any insignificant variable? If yes, regress again, by dropping the variable. Will dropping that variable increases the adjusted R square?

Q. a. The height of the students in a certain class is following normal distribution with mean height as 165 cm and standard deviation of 25 cm. There are 60 students in that class. Determine

i. The number of students whose height is more than 158 cm. ii. The number of students whose height is lying between 155 and 172 cm.

3. b. Find the lowest height among the tallest 5 student in a class.

Q. 1. A dealer of Mobile TV has the following items in inventory as on March 31,2018

Item Quantity Cost Price per unit Market price per unit
Nokia, 50, 100000, 98000
Samsung, 70, 88000, 90000
Sony, 100, 120000, 115000
Motorola, 80, 75000, 76000

Discuss the accounting standard which talks about inventory valuation. Also, find out and define the overall value of inventories as per the applicable accounting standard.

2. Define and Discuss the concepts of prepaid expenses and outstanding expenses and their impact on the income statement and Balance Sheet of an Entity? In case of firm A which largely has the balance of prepaid expenses and another firm B which largely has the balance of outstanding expenses, what does this reflects? Discuss

3. a. A logistics company sold a car of Rs 2.5 lacs. The company had purchased the car three years back for Rs 10 lacs and had depreciated the same using straight line method of depreciation, assuming its useful life to be five years and a residual value of Rs77760. Calculate the WDV after charging depreciation for third year, accumulated depreciation for three years and profit on sale, if any.

b. Consider the following transaction pertaining Ammar’s business-

1. started business with cash Rs 3 lacs
2. Purchased goods for cash Rs 1.2 lacs
3. purchased goods on credit Rs 60000
4. purchased furniture for cash Rs 20000
5. deposited RS 50000 in the bank

Perform transaction analysis for each transaction undertaken and present accounting equation for these transactions.

Q. What is sampling distribution? An automobile manufacturer claims that a particular model gets 28 KM per liter of petrol, but the Environmental Protection Agency, using a sample of 50 automobiles of this model, finds the sample mean to be 26.8 km/ltr. From previous studies, the population standard deviation is known to be 5 km/ltr. Could we reasonably expect (within 2 standard errors) that we could select such a sample if indeed the population mean is 28 km/ltr? Justify.

Q. Raj studios a Tollywood casting company, is selecting a group of extras for a movie. The ages of the first 30 men to be interviewed are.

50 56 55 54 55 61 49 52 57 60 51 59 56 57 56
62 52 54 55 49 52 61 60 51 57 56 59 52 54 49

The director of the movie wants men whose ages are grouped around 50 years. The director suggests that a standard deviation of 3 years would be acceptable. Does this group of extras qualify to the director’s requirement?

Q. Historically, diesel has mostly been cheaper than petrol in South Africa, though this has not always been the case, and not a trend seen around the world. One of the key differences in the pricing of diesel versus petrol, is that diesel prices reflect wholesale prices, not the price you would pay at the pumps. For example, the wholesale inland diesel price for August was at R10.96 at the beginning of the month, while Caltex’s retail version – Caltex 50 diesel with Techron – sells at R11.33 per litre. Over the past decade, both the petrol and diesel prices have seen some significant fluctuations, but petrol (95 grade) has seen the biggest overall increase, having jumped 75.4% since 2006.

The graph and table below show how the prices have changed year-on-year, between August 2006 and August 2016.

Year, Petrol-Unleaded 93, Petrol-Unleaded 95, Diesel 0.05%
2006, R6.92, R7.04, R6.54
2007, R6.88, R7.01, R6.51
2008, R10.20, R10.40, R11.27
2009, R7.52, R7.69, R6.65
2010, R8.02, R8.17, R7.38
2011, R9.91, R10.09, R9.30
2012, R10.83, R11.04, R10.25
2013, R13.32, R13.55, R12.48
2014, R14.08, R14.33, R12.84
2015, R13.01, R13.26, R10.94
2016, R12.08, R12.35, R10.96

Source: Department of Energy; Inland prices, August

The fuel price is affected by two major components: the global oil price, and the currency exchange rate between the rand and the dollar. Between 2014 and 2016, fuel prices (both diesel and petrol) have shown a year-on-year decline, boosted by a much lower global oil price, which has dropped below $50 a barrel, with little hope that it will balloon past that level in the near future. However, much of the benefit delivered by lower oil prices has been undone by weakness in the rand – brought about by a struggling economy, poor growth policies and a number of political scandals involving president Jacob Zuma. (Source: https://businesstech.co.za/news/energy/134400/petrol-vs-diesel-prices-in-south-africa-2006-2016/)

a. Explore the trend in the petrol price (for both unleaded 93 and unleaded 95) using regression trend analysis. Using the data, forecast the petrol price for 2017, 2018 and 2019.
b. Explore the trend in the diesel price using regression trend analysis. Using the data, forecast the diesel price for 2017, 2018 and 2019. Out of the three regression models, which model is the strongest in predicting the fuel price?

Q) The sample data from a research survey conducted in various cities on the amount of time 13-15 year-old children spent with mobiles are as follows:

City Time with mobiles (hours per week)
Hyderabad, 46
Mumbai,50
Pune,46
Bangalore,54
Bhubneshwar,42
Indore,30
Bhopal,42
New Delhi,50
Chandigarh,46

For the above sample, determine the following measures: i. The mean ii. The standard deviation iii. The mode iv. The 75th percentile Based on your calculations comment on the time spent on mobile. (10 Marks)

Q) ‘Mumbai Ice Cream an ice cream store gives relationship between ice cream sold and temperature. The store has taken a sample of a week’s data. Below you are given the results of the sample

Day, Cones Sold, Temperature
1,350,110
2,200,100
3,210,90
4,100,80
5,80,70
6,70,60
7,50,50

i. Which variable is the dependent variable? ii. Compute the least squares estimated line. iii. Is there a significant relationship between the sales of cones and temperature? iv. Predict sales of a 95 degree day.

Q) According to one of the recent study conducted by an academic researcher on international placement of students from leading institutes in India there is a high variation in the salary offered by institutes. The following details have been gathered from the placement institute of the colleges. The researcher wants to understand the trends with regard to international placement based on the data he has gathered.

Amount (in USD in lakhs per annum), Age, Marital Status, Type of institute, Gender
2, 35, Single, University, Male
5, 24, Married, PGDM, Male
3.5, 29, Married, University, Female
5, 26, Single, University, Male
4, 26, Married, PGDM, Female
8, 25, Single, PGDM, Female
15, 34, Married, PGDM, Male
3, 26, Single, PGDM, Male
7, 23, Single, PGDM, Male

a. Using descriptive statistics explore salary, and identify factors that appear to influence the amount of the salary received. (5 Marks)
b. Do a correlation analysis between ‘Amount’ and ‘Age’ and interpreted the coefficient of correlation.

Q)Here’s the data for teams in the National Basketball Association (NBA):

Team Revenue (USD Mn.) Valuation (USD Mn.)
Atlanta 103 306
Boston 144 433
Charlotte 96 278
Chicago 168 511
Cleveland 159 476
Dallas 154 446
Denver 115 321
Detroit 171 479
Golden State 113 315
Houston 160 470
Indiana 97 281
Los Angeles Clippers 102 295
Los Angeles Lakers 209 607
Memphis 88 257
Miami 126 364
Milwaukee 91 254
Minnesota 96 268
New Jersey 92 269
New Orleans 95 267
New York 202 586
Oklahoma City 111 310
Orlando 107 361
Philadelphia 115 344
Phoenix 148 429
Portland 121 338
Sacramento 109 305
San Antonio 133 398
Toronto 133 386
Utah 118 343
Washington 110 313

1) For the data on revenue and valuation of teams in the National Basketball
Association (NBA), conduct the following analysis:
i. Determine the measures of central tendency and of dispersion for revenue
and valuation.
ii. Provide the five-number summary i.e. the minimum, 1st quartile, median,
3rd quartile and maximum value for revenue.
Interpret the above results and comment on how the data is distributed.

2. For the same data on NBA revenue and valuation given above:
i. Is there a strong association between revenue and valuation?
ii. Create a scatterplot diagram depicting the association between the two variables.
iii. The franchise owners want to understand if the valuation is dependent on revenue. How can you assess this?
iv. Using the regression equation, predict the valuation of a team whose revenue was USD 300 mn.

Q) For the data on 30 mutual funds given above, conduct the following analysis:
i. Determine the measures of central tendency and of dispersion for the five variables.
ii. Provide the five-number summary i.e. the minimum, 1st quartile, median, 3rd quartile and maximum value for asset size.
Interpret the above results and comment on how the data is distributed.

Assets Expense Ratio Return 2006 3-Year Return 5-Year Return
904.8 1.51 4.6 10.7 8.1
675.9 1.28 8.5 11.9 7.3
909.7 0.80 13.1 10.4 6.3
52.2 1.50 11.6 10.3 6.4
8411.5 0.63 10.9 12.4 8.0
282.3 1.22 7.1 10.2 8.0
9870.7 0.86 12.3 15.0 7.7
424.8 1.13 12.3 11.0 6.2
15422.9 0.72 14.0 10.2 6.2
497.9 1.36 8.6 12.0 7.3
547.3 1.09 7.5 12.8 7.2
5527.1 0.41 11.2 10.2 6.5
22592.9 0.46 12.3 13.0 8.4
240.8 1.42 4.4 10.3 6.6
2403.4 0.93 8.0 10.1 4.3
233.3 1.33 6.5 9.4 5.4
71.2 0.15 15.4 6.6 5.0
506.9 1.15 11.2 9.3 4.5
221.6 1.12 13.2 8.9 4.7
434.9 1.19 14.2 12.3 7.1
7834.2 0.56 13.7 9.6 5.5
152.1 1.34 12.4 9.6 4.6
815.4 0.73 13.0 8.9 4.5
85.7 0.45 13.2 9.6 4.0
166.1 1.41 3.3 7.8 5.3
47.2 0.74 8.1 10.8 5.7
6955.2 0.87 7.8 10.7 5.8
135.4 1.25 14.6 8.2 5.8
142.0 1.18 9.2 9.7 5.6
601.8 1.00 9.7 7.9 3.8

Q) For the same data on mutual funds given above:
i. Is there a strong association between asset size and expense ratio?
ii. Create a scatterplot diagram depicting the association between the two variables.
iii. Using the regression equation, predict the 5-year return of a fund whose 3-year return was 8%.

Q) There are 300 students in an online MBA program for working professionals, for whom the attendance in online classes is 70%, i.e. on an average, 210 students are present in an online session. Fifty new students are admitted in this batch.
a. What is the probability of attendance being at least 70% among the new students, thus ensuring the overall attendance does not fall below 70%?
b. The Program Dean thinks that this probability will increase, if the new batch size is 40 instead of 50 students. Is he right in assuming so?

Q) Assume there are 400 athletes in a training camp, who are required to attend the morning drill starting at 4 am. The attendance in morning drills is 70%, i.e. on an average, 280 athletes are present. Fifty new athletes are admitted in this batch.

a. What is the probability of attendance being at least 70% among the new athletes, thus ensuring the overall attendance does not fall below 70%?
b. The training coach thinks that this probability will increase, if the new batch size is 40 instead of 50 students. Is he right in assuming so?

Q) Suppose you want to design a salad having two main items, lettuce and tomato. Suppose that each gram of lettuce provides 2 units of vitamins and 2 units of minerals and each gram of tomato provides 1 unit of vitamins and 2 units of minerals. The cost of lettuce is 100 Rs/gram and the cost of tomato is 20 Rs/gram.

The salad must provide at least 8 units of vitamins and 10 units of minerals. How many grams of each item should be provided in order to meet the requirements of vitamins and minerals for the least cost? What will this salad cost? Use the graphical method. Present both primal and dual forms, including their graphs.

Q) You are required to develop a multiple linear regression model based on the data given below, reporting about multicollinearity to refine your model, if required. Consider Profit (Rs.) as the dependent variable. Interpret your results. Suppose your dependent variable (Profit) takes values of “High profit” (Profit > Rs 1,35,000) or “Low profit”: in such case what type of regression model would you like to use and why? (For this part of the question, you need not develop the model or interpret the results.)

PLEASE REFER THE TABLE BELOW

Q) Suppose that you are required to plan the least-cost transportation from the manufacturing centers to the outlets. The transportation cost matrix is given below.
Destination 1 Destination 2 Destination 3 Supply Origin 1 20 17 4 120 Origin 2 35 10 5 60 Demand 40 30 110 180
a. Find the initial basic feasible solution using Vogel’s Approximation Method.
b. Find the final (optimal) solution using Modified Distribution method.

Question: Solve by Simplex Method:- a) Find the Optimum Solution. b) Perform coefficient sensitivity analysis on variables X1, X2, X3 C) Write the dual to the above problem and read out the values of the dual variable from the final simplex table of the primal. Also prove that dual to the dual is primal.

Question: a) A player aims a shot at a pile of stones in order to break the pile. He is given 2 shots to aims at the pile of stones. If the accuracy of the aim of the player is such that he will break the pile on 80% of the occasions, determine the probability distribution of the player breaking either 0, or 1 or 2 times if he throws two times. Find the mean and the variance of this binomial distribution.
b) The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport. At the present time, the noise level per jet takeoff in one locality near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 6 decibels.
i) What is the probability that a randomly selected jet will generate a noise level greater than 108 decibels in this locality?
ii) What is the probability that a randomly selected jet will generate a noise level of between 92 and 110 decibels?
iii) Between which two noise levels centered around mean do 95% of the jets emit noise.
iv) Suppose a regulation is passed that requires jet noise in this locality to be lower than 105 decibels 95% of the time. Assuming the standard deviation of the noise distribution remains the same how much will the mean level of noise have to be lowered to comply with the regulation?

Question: The following table gives the activities in a construction project and other relevant information. i. Draw an arrow diagram for the project. ii. Calculate Earliest & Latest start time, Earliest and Latest finish time for each activity. Calculate all the Total Float, Free Float, Interfering Float and Independent Float for each Activity.

Question: a) Explain the case of quantitative techniques in business decision making? b) What is linear programming? What are its major assumptions and limitations?

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