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(Department of mathematics and Statistics)
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Course: Statistics (394) Semester: Spring, 2012
Level: F.A. Total Marks: 100
Pass Marks: 40
ASSIGNMENT No. 1
(Units 1–5)
Q.1 a) Define and explain the terms: Descriptive and inferential Statistics.
b) Expand the following summation and product notations.
i)
c) Following statements are true or false, if false, write correct i) The numerical quantity calculated from the population is called statistics. ii) Statistics deals with single fact. iii) Primary data and ungrouped data are same. iv) Height of the student is a quantitative and continuous variable. v) A small part of the population is called subset.
Q.2 a) The following information is available about the age in years and their weights in kilograms (age, weight). Make a scatter plot and appropriate bivarite frequency distribution. (20, 60), (15, 55), (14, 45), (17, 60), (16, 48), (22, 70), (16, 63), (14, 55), (18, 57), (19, 67), (21, 67), (17, 65) (13, 60), (15, 60), (17, 49), (19, 65), (23, 73), (21, 65), (22, 70), (14, 50), (16, 60), (19, 59), (15, 62), (17, 59), (24, 75)
b) Construct a Histogram for the following frequency distribution giving the steps involved.
Mid values (x) 32 37 42 47 52 57 62 67 Frequency (f) 3 17 28 47 54 31 14 4
Q.3 a) Calculate the 5th^ percentile, Quartiles, mode and Coefficient of Variation for the following data
Groups Frequency Groups Frequency 0-4.9 3 25-29.9 13 5-09.9 4 30-34.9 13 10-14.9 9 35-39.9 5 15-19.9 11 40-44.9 2 20-24.9 15 45-49.9 2
b) Define the terms i) Absolute dispersion ii) Relative dispersion.
Q.4 a) Write down the properties of arithmetic mean and variance. What is the importance of coefficient of variation?
b) Computer calculated mean and standard deviation from 20 observations as 42 and 5 respectively. It was later discovered at the time of checking that it had copied down two values as 45 and 38 whereas the correct values were 35 and 58 respectively. Find the correct value of co-efficient of variation.
c) Given that
Compute the first four moments about mean as well as coefficient of skewness and kurtosis of the distribution.
Q.5 a) What is an index number? Give the uses of an index number.
b) Compare the following concepts: i) Simple and composite index ii) Fixed and chain base method
c) Calculate Laspeyre’s, Paasche’s and Fisher’s ideal index for the following data taking 1992 as base.
Year Item
Average Price (Rs) Quantity (Kg) Wheat flour 4.38 4.57 20 16 Rice 14.15 15.58 10 12 Moong Pulse 18.67 17.28 1 1 Gram Pulse 10.41 16.36 1 1
iii) Find the mean and standard deviation of the binomial distribution ( q + p )n
Q.5 a) Five balls are drawn from a box containing 4 white and 7 black balls. If X denotes the number of black balls drawn, then obtain the probability distribution of X. Find the mean and variance of this distribution.
b) A Committee of size 5 is to be selected at random from 3 women and 5 men. Find the expected number of women on the committee.
c) A box contain five slips of paper marked 1, 2, 3, 4 and 5. Two slips are selected without replacement; list the possible values for each of the following random variables. i) The sum of the two numbers on two slips. ii) The difference between the first and second number.
