BUSINESS MATHEMATICS AND STATISTICS - I
Descriptive Questions
FYBCOM
Interest and Annuity
Short-Answer Questions
1. What is interest?
2. Differentiate between simple and compound interest.
3. How is rate per annum calculated on an interest?
4. Define ‘sinking fund’ and ‘amortization’ with the help of simple examples.
5. Write the formula for finding the simple interest and amount of a given sum in a
given time.
6. Write the formula for finding the interest and amount of a given sum at compound
interest.
7. Define simple annuity. How is present value of annuity calculated for n years?
8. What is perpetuity?
9. Write the formula for finding effective rate of interest.
10. Briefly define EMI along with its formula and specifications.
Long-Answer Questions
1. Find in what time a sum of money trebles itself at 5 per cent per annum compound
interest.
2. A sum of 20,000 is borrowed at 4 per cent per annum compound interest.
The principal and interest are to be repaid in 25 equal annual instalments beginning
one year hence. Find the yearly payment.
3. If Re 1 was deposited in the Post Office Savings Bank on 1 April 1903, what would it amount to on 1 April 1933 if a compound interest at 3 per cent per annum was allowed?
4. An officer drawing a salary of 1500 per month in a pay scale of
1300 – 100 – 1800 borrowed from his employer on 1 January 1964, a sum of 15,000 for the purchase of a car. The money is to be recovered by making a deduction of 20 per cent from his salary every month. If the interest is calculated at the rate of 5 per cent on 31 December each year on the highest amount due on any day in the preceding year and added to the balance due, when will the officer receive his full salary? Note that the first deduction is made from the salary of January paid on 1 February 1964 and his increment falls due on 1 July.
5. A sum of money invested at compound interest amounts to 21,632 at the end of 2nd year and to 22,497.28 at the end of the third year. Find the rate of interest and sum invested.
Shares and Mutual Funds
Short-Answer Questions
1. State any four essential features of a share.
2. Explain preference shares on the basis of redemption.
3. What are the rules to issue equity shares with differential rights?
4. Outline any three differences between equity shares and preference shares.
5. What is subscribed capital?
6. Define mutual funds and its operation.
7. How is a mutual fund managed?
8. What is meant by index funds? What are its advantages?
9. Define the role and the requirements of a sponsor.
10. What is NAV? Give any two factors influencing the NAV.
11. What are balanced funds?
12. How can close-ended schemes be converted into open-ended schemes?
13. What is meant by lacunae in regulations?
14. Explain the advantages of mutual funds.
15. What is the role of SEBI in regulating the mutual fund industry?
Long-Answer Questions
1. What is a 'share'? Discuss their different classes and the essential features of a share.
2. Explain the concept that a share has a nominal value and bears a distinct number.
3. Explain the significance of preference shares giving appropriate examples.
4. Distinguish between equity shares and preference shares, and equity shares and share capital giving appropriate examples.
5. What are the objectives of mutual funds? Describe the benefits of mutual funds.
6. Analyse the different types of mutual funds and give examples.
7. What are the five distinct phases of growth of mutual fund industry in India? Justify your answer giving appropriate examples.
8. How the formation and operations of the mutual funds are governed by the Securities Exchange Board of India (SEBI) Mutual Funds Regulation? Justify your answer giving appropriate examples.
9. Critically evaluate the functioning of mutual funds in India.
10. How is NAV calculated? Discuss the importance of NAV.
11. How do the mutual funds deploy their money? What are the regulations regarding the investment of mutual funds?
Population and Sample
Short-Answer Questions
1. What is business statistics?
2. Explain any two functions of statistics.
3. How is statistics used in production, marketing and purchasing?
4. Explain the terms sample and variable.
5. What is sampling? What are the benefits of sampling in statistics?
6. What is the relation between census and sampling?
7. Define the term variable and random variable. Give examples.
8. What are the benefits of sampling? Outline the methods of sampling.
9. List the methods used in selecting a sample and the various sampling techniques.
10. What is deliberate sampling?
11. What are the methods used for objective selection of random sample?
12. How will you explain sampling and non-sampling errors?
13. Elaborate on any two sampling techniques.
14. What are the implications of simple random sampling?
15. Explain the sampling theory.
16. Give details on standard error and sampling distribution.
17. What is a t-test?
18. What are the various methods of data collection?
19. Why is the questionnaire method used? Why are questionnaires useful?
20. List any six standard errors of statistical calculations.
Long-Answer Questions
1. Discuss the characteristics of business statistics? Explain giving relevant examples.
2. Briefly explain the role and scope of Statistics in Economics, Management Science and Industry.
3. Discuss the uses of statistics in business and commerce.
4. What are the different sampling techniques? Elaborate giving appropriate examples.
5. Explain the meaning and significance of the concept of ‘Standard Error’ in sampling analysis.
6. Why is sampling necessary in statistical investigations? Explain the important methods of sampling commonly used.
7. ‘Sampling is a necessity under certain conditions.’ Explain this by giving examples. Also indicate the advantages of stratified sampling over random sampling
Measures of Central Tendencyand Measures of Dispersion
Short-Answer Questions
1. Explain the terms raw data, attributes and variables.
2. How is data classified?.
3. Define frequency distribution.
4. What is cumulative frequency distribution?
5. Explain relative frequency distribution.
6. Elaborate on histogram and ogive curves.
7. What is mean? Write three advantages and disadvantages of a mean.
8. What is a median? Give advantages and disadvantages of median.
9. What is mode? Give advantages and disadvantages of mode.
10. Define the terms Geometric Mean (GM) and Harmonic Mean (HM),
11. What are the characteristics of a measure of dispersion?
12. How can an absolute measure be converted into a relative measure?
13. Outline the limitations of range.
14. State any two uses of range.
15. How is Mean Deviation (MD) calculated?
16. List out the merits and demerits of mean deviation.
17. What is coefficient of mean deviation?
18. Define Quartile Deviation (QD).
19. Explain standard deviation. Why is it used in statistical evaluation of data?
20. How calculation of Standard Deviation (SD) differs from Mean Deviation (MD)?
21. What is skewness? Explain the different types of skewness.
22. How will you measure skewness?
23. Define the term kurtosis.
Long-Answer Questions
1. Differentiate between primary data and secondary data. Under what
circumstances would secondary data be more useful than primary data?
2. Describe a project in which it would be necessary to use primary data rather
than secondary data. Give reasons.
3. Discuss about raw data, attributes and variables giving appropriate examples.
4. Explain the method of classification of data giving appropriate examples.
5. A professor in statistics class was rated by his 20 students on a scale of 1 to 5
where the rating of 5 was considered as excellent and the rating of 1 was
considered as poor with an increasing scale from poor to excellence. These
ratings are recorded individually in the following table.
4 3 1 1 4 5 2 2 4 4
2 3 3 4 3 5 4 4 5 3
(i) Construct a frequency distribution for this data.
(ii) Draw a frequency polygon for this data.
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