This document contains sample questions from quantitative methods exams from 2009 and 2010. It includes questions on topics like constructing charts, calculating means, variances, standard deviations, correlations, and regressions from data sets. It also includes questions on index numbers, time series analysis, probability distributions, and fitting trends to time series data. Students were asked to show calculations and proofs for quantitative analysis concepts.

1. Quantitative Methods (First Half) – 2009
1. Answer any four questions: 5 × 4
(a) Construct a pie-chart for the following data:
Principal Exporting Countries of Cotton (1,000 bales) – 1955-56
USA India Egypt Brazil Argentina
6,367 2,999 1,688 650 202
(b) The arithmetic mean of two observations is 25 and their geometric mean is 15. Find (i) their
harmonic mean and, (ii) the two observations.
(c) The following table gives the marks in Management obtained by boys and girls studying in a
college. Find the standard deviation of the marks in Management of boys and girls taken
together.
Boys Girls
Number 400 100
Average marks 68 65
Variance of marks 9 4
(d) State the basic properties of simple correlation coefficient.
(e) Fit a straight line to the following data by the method of least squares:
x : 15 20 25 30 35
y : 12 14 18 25 31
(f) Two cards are drawn from a full pack of 52 cards. Find the probability that (i) one is a heart
and the other is a diamond, and (ii) both are red cards.
2. Answer any two questions: 10 × 2
a. i. Find the mean and variance of Poisson distribution.
ii. Prove that the correlation coefficient does not depend on the origin or scale of the
observations.
b. i. Show that neither Laspeyer’s formula nor Paasche’s formula obeys time reversal or
factor reversal test.
ii. Find the median and the median class of the data given below:
Class Boundaries : 15-25 25-35 35-45 45-55 55-65 65-75
Frequency : 4 11 19 14 6 2
Quantitative Methods (First Half) – 2010
1. Answer any four questions: 5 × 4
(a) If x1 and x2 are two positive values of a variable, prove that their geometric mean is equal to the
geometric mean of their arithmetic mean and harmonic means. 5
(b) (i) Define median for a grouped frequency distribution.
(ii) Find the median of the simple series: 32, 22, 29, 17, 40, 26, 21, 20. 2½ + 2½ = 5
(c) Define standard deviation of a set of observations and for a frequency distribution. What are the
important properties of standard deviation? 5
(d) Prove that the correlation coefficient ‘r’ lies between -1 and +1. 5

2. (e) Derive the linear regression equation of ‘y’ on ‘x’, where ‘y’ is the dependent variable and ‘x’ is
the independent variable. 5
(f) Examine whether Fisher’s ideal index number satisfies Time reversal and Factor reversal tests.
5
2. Answer any two of the following questions: 10 × 2
(a) (i) Find the mean and variance of binomial distribution.
(ii) The standard deviation calculated from a set of observations is 80, what is the sum of the
squares of these observations? 6 + 4
(b) (i) The arithmetic mean calculated from the following distribution is known to be 67.45
inches. Find the value of f3.
Height (inches) : 60-62 63-65 66-68 69-71 72-74
Frequency : 15 54 f3 81 24
(ii) Fit a straight line trend by the least squares method to the following data:
Year : 1969 1970 1971 1972 1973 1974 1975
Production : 76 87 95 81 91 96 90
Estimate the production for 1976. 6 + 4
(c) (i) Defining the concepts of mutually exclusive, exhaustive and equally likely outcomes, state
the classical definition of probability.
(ii) Find the mode of the following distribution:
Daily wage : 5-6 7-8 9-10 11-12 13-14
Frequency : 10 30 41 29 5
5 + 5
Quantitative Methods (First Half) – 2010
1. Answer any four questions: 5 × 4
(a) What do you understand by Histograms, Frequency Polygon and Ogive?
(b) Prove that the correlation coefficient does not depend on the origin or scale of the
observations.
(c) Find the mean and the standard deviation of the first ‘n’ natural numbers.
(d) Examine whether Laspeyre’e and Paasche’s price index satisfies time reversal and factor
reversal tests.
(e) Differentiate between (i) Variable and attribute, and (ii) Primary data and secondary data.
(f) Prove that standard deviation is independent of any change of origin, but is dependent on
the change of scale.
2. (a) (i) Find the mean and variance of Poisson distribution.
(ii) The mean and standard deviation of 20 items is found to be 10 and 2 respectively. At
the time of checking it was found that one item 8 was incorrect. Calculate the mean and
standard deviation if it is replaced by 12 and if the wrong item is omitted.
5 + 5
(b) (i) Prove that the standard deviation calculated from two values x1 and x2 of a variable x is
equal to half of their difference. 4

3. (ii) When two unbiased coins are tossed, what is the probability of obtaining 3 heads and not
more than 3 heads? 4
(iii) If two groups contain n1 and n2 observations with means and and standard deviations
and respectively, then what is the standard deviation of the composite group, taking
n1 and n2 observations together? 2
(c) (i) Find the correlation coefficient between x and y.
x : 5 7 9 11 13 15
y : 1.7 2.4 2.8 3.4 3.7 4.4
3
(ii) Calculate arithmetic mean and median of the frequency distribution given below. Hence
calculate the mode using empirical relation between the three.
Class
Limits
: 130-134 135-139 140-144 145-149 150-154 155-159 160-164
Frequency : 5 15 28 24 17 10 1
5
(iii) Mention the various mathematical curves and its mathematical forms for determining trend
of time series data. 2
Quantitative Methods (First Half) – 2009
1. Answer any four questions: 5 × 4
(a) Prove that standard deviation is independent of change of origin, but is dependent on the
change of scale.
(b) Establish the relationship between correlation coefficient and two regression coefficients.
(c) With the help of the data given below calculate the price index numbers by (i) Paasche’s
method, and (ii) Laspeyre’s method.
Commodity 2001 2002
Price (Rs.) Quantity (kgs) Price (Rs.) Quantity (kgs)
A 20 8 40 7
B 50 10 60 5
C 40 15 50 10
D 20 20 20 15
(d) ‘Index numbers are economic barometers’- Explain this statement and mention the
limitations of Index numbers (if any).
(e) State the components of Time Series.
(f) ivalWhat do you understand by the terms – skewness and kurtosis?
2. Answer any two questions from the following: 10 × 2

4. (a) In the frequency distribution of 100 families given below, the number of families
corresponding to expenditure groups 20-40 and 60-80 are missing from the table. However,
the median is known to be 50. Find the missing frequencies:
Expenditure : 0-20 20-40 40-60 60-80 80-100
No. of families : 14 ? 27 ? 15
(b) The following table relates to the tourists arrivals (in millions) during 1994 to 2000 in India:
Year : 1994 1995 1996 1997 1998 1999 2000
Tourists arrivals : 18 20 23 25 24 28 30
Fit a straight line trend by the method of least squares and estimate the number of tourists
that would arrive in the year 2004.
(c) (i) Find the mean and variance of the Poisson distribution.
(ii) When three unbiased coins are tossed, what is the probability of obtaining two heads?
7 + 3