B.Sc-B.Sc Statistics 1st Sem Descriptive Statistics(University of Pune, Pune-2013)
[4317] - 13
F.Y. B.Sc.
SEAT No. :
[Total No. of Pages : 4
STATISTICS/STATISTICALTECHNIQUES
Descriptive Statistics
(Paper - I) (2008 Pattern)
Time : 3 Hours] [Max. Marks :80
Instructions to the candidates:
1) All questions are compulsory.
2) Figures to the right indicate full marks.
3) Use of statistical tables and calculators is allowed. 4) Symbols have their usual meanings.
5) Graph papers will be supplied on request.
Q1) Attempt each of the following: [4 x 1 = 4]
a) Choose the correct alternative for the following:
i) The type of sampling approach where each person in the sampling
frame has an equal chance of being selected is best described as:
1) Systematic sampling.
2) Stratified random sampling. 3) Simple random sampling. 4) Cluster Sampling.
ii) Box plot helps to judge the
1) Spread.
2) Symmetry.
3) Central value. 4) All the above.
iii) Which of the following is not a central value?
1) Arithmetic mean. 2) Median. 3) Mode.
4) Standard Deviation.
P.T.O.
iv) Karl Pearson’s coefficient of correlation lies between.
1) 0 to 1.
2) –1 to 1.
- ¥
- ¥ to ¥
b) State whether the following statements are true or false: [4 x 1 = 4]
i) Histogram cannot be drawn for a frequency distribution having open
end classes.
ii) Arithmetic mean can be determined graphically. iii) The first central moment is zero.
iv) For a symmetric distribution the quartiles are equispaced.
c) Define attribute and variable. [2]
d) For two attributes A and B if (A) = 100 (B) = 150 (AB) = 60 and
N = 500, find (a B) . [2]
e) Calculate arithmetic mean for a group of 10 observations if
å(xi -5)=20 . [2]
f) Explain positive correlation with a suitable example. [2]
Q2) Attempt any four of the following:
a) Explain the following terms:
i) Class limits. ii) Class width.
iii) Class frequency. iv) Open end class.
b) Explain systematic sampling with illustration.
[4 x 4 = 16]
- Suppose {(xi, fi )i=1,2,3.....k} is a frequency distribution. Show that
arithmetic mean does not change if each frequency is doubled.
d) The daily expenditure of 120 families is given below:
Expenditure 100-120 120-140 140-160 160-180 180-200
No. of families 12 - 38 - 14
If the mode of the distribution is 153, find the missing frequencies.
e) Prove that the sum of squared deviation is least when taken from the
arithmetic mean.
[4317]-13 2
f) Explain the concept of skewness. Draw the sketch of a frequency
distribution and show the positions of the mean, median and mode when
the distribution is
i) Symmetric.
ii) Positively skewed.
Q3) Attempt any four of the following: [4 x 4 = 16]
a) Define quartile deviation and standard deviation. State the formula for
each in case of ungrouped (raw) data and grouped frequency distribution.
b) The range, arithmetic mean and standard deviation of a group of 10
observations is 20,62 and 10 respectively. If each observation is decreased by 5, find the value of range and the coefficient of variation for the changed data.
c) Describe scatter diagram and explain its use to study correlation.
d) Define raw and central moments of a frequency distribution. Express the
4th central moment in terms of the first four raw moments.
e) Compute Fisher’s price index number for the year 1995 considering
year 1990 as the base year for the following data:
Commodity Quantity Price
1990 1995 1990 1995
A 15 12 15 22
B 14 4 20 27
C 10 8 4 7
f) Define median and state any two demerits of median as a measure of
central tendency.
Q4) Attempt any two of the following: [2 x 8 = 16]
a) i) What is meant by association of two attributes? How is it measured?
ii) In a report of consumer preference of two varieties of perfumes A
and B, it was given that out of 500 persons surveyed 410 preferred variety A, 380 preferred variety B and 270 persons liked both. Are
the data consistent?
b) i) For a bivariate data the regression equations are given by 3X-Y-5 = 0
and 4X-3Y = 0. Find the arithmetic means of X and Y. Also find the correlation coefficient between X and Y.
ii) Define Spearman’s rank correlation coefficient assuming no ties
and derive an expression for it.
[4317]-13 3
c) Two groups with n1 and n2 observations have the arithmetic means X1
and X2 the standard deviationss1 and s2 respectively. Derive formula
for combined standard deviation in each of the following cases:
i) X1 = X2 .
ii) n1 = n2.
iii) n1 = n2 and X1 = X2 .
- n1 = n2 , X1 = X2 ands1 = s2 .
d) i) Write a note on kurtosis.
ii) For a symmetric distribution, with usual notation prove that,
m3′ =3m2+ (m1)2
m1′
.
Q5) Attempt any two of the following: [2 x 8 = 16]
a) i) Define Index Numbers and state its uses.
ii) Weight in mg of 25 residuals are given below:
50,46,31,49,33,42,55,37,36,35,65,57,27,37,42,33,51,46,31,37,51,56,51,43,48,
Construct a stem and leaf chart.
- For a given bivariate data (xi , yi ),i =1, 2,..., n, derive the expression for
the line of regression of Y on X.
Given that r = 0.3,å(X-X)(Y-Y)=108,sy =3 and å(X-X)2 = 400.
Find number of pairs of observations.
With usual notation prove that, (byx +bxy)/2³ r if r > 0.
Explain the procedure of fitting the curve y = abx for a bivariate
data (xi, yi ),i =1,2....n.
Find quartile deviation if Bowley’s coefficient of skewness is•0.36, median = 16.5 and Q1 = 13.8.
| Earning: Approval pending. |
