Statistics Question paper
Q 1.Give a brief account o f statistics mentioning utilities to other social s ciences Q 2. Explain the limitations of statistics. Q 3.Explain the role of statistics in agriculture. Q 4.a) What is measure of central tendency? b)When do you say that an a verage is stable? c)Write any two properties of arithmetic mean. d)Write the formula for computing median in case of continuous frequency distribution. e)The mean mean of a set of seven observations is ten ten and mean of a set of 3observations is 5 .What is the mean mean of combined combined set? Q 5. Find the missing missing frequency of the following distribution ,given that arithmetic mean is eleven. Class interval
frequency
0-----4
3
4-----8
10
8-----12
--
12----16
14
16----20
7
20----24
1
Q 6. Out of 15 candidates 5 failed in a test .Those who passed in the test have marks marks 9 , 6,7,8.9.6,5,4,7,8 Find the median median of all the fifteen candidates. Q 7. Systolic B.P of the group o f men are as recorded below Group
number of men
1
113
2
121
A.M 159mm 149mm
S.D 22.4mm 20mm
Find the combined mean and standard deviation. Q 8 .The mean and standard deviation o f ten values are 40 and 4 respectively. Lat Latter ter it was found that a value 34 was wrongly recorded as 43 .Find the actual mean and standa rd deviation. deviation.
Q 9. a) b)
If
n=10
find coefficient of variation.
Explain the object of measuring dispertion.
Q 10. a) What is symmetric distribution? b) Which tail of the distribution is lengthier for negatively skewed distribution? c) Given karl pearsons coefficient of skewness = --0.4
mode =52ft and SD = 5ft find the
value of mean d) What is the need for measure of skewness? e) What is skewness?What are different types of skewness? Q 11. Explain the following with the help of examples. 1) Equally likely events. 2)Mutually exclusive events 3)Exhaustive set of events 4)Random experiment Q 12. a) Give classical definition of probability. b) A bag has 9 tickets numbered 1,2,3,4,5,6,7,8,9,.Two tickets are drawn at random from the bag, find the probabilit y that both the numbers drawn are 1)even 2)odd Q.13. A card is drawn from a .pack of 52 playing cards,find the probability that the drawn card is 1)a spade or a king
2) a king or a queen
Q.14. a)What is conditional probability? State multiplication theorem on probability. b)A card is drawn from a pack of 52 cards 1)what is the probability that it is a heart? 2)If it is known that the card drawn is red, what is the probability that it is heart?
Q 15. (a) If P (A) = 0.8
P(B) = 0.5 P(AUB) =0.9 Find P(A/B) . Are A&B independent events.?
(b) The probabilities of three drivers driving home safel y after consuming liquor are ¾, 3/5, 4/5 respectively. One day three drivers start home after consuming liquor in a party. Find the probability that all the three drive home safely,
Q 16. (a) A random variable X takes the value 1&0 with respective probabilities P & 1-P find its mean, variance and standard deviation. (b) A bag contains 3 green & 2 r ed balls. A man throws 2 balls at random from the ba g. If he is to receive Rs.20 / - for every green ball he throws and Rs. 10/- for every red one what is his expectation?
Q 17. (a) For two independent random variables X & Y. Show that (1) cov (xy) = 0
(2) correlation coefficient r = 0
b)A person by paying Rs5/= enters into game of shooting, if he hits the target with one shot he gets Rs25/= otherwise he gets nothing. If his probability of hitting the target is 1/7, find his expected loss. Q 18. (a) What is correlation? Explain different types of correlation giving an example for each. (b) Define Karl pearsons coefficient of correlation. What are its properties? Q 19. Explain spearman¶s coefficient of Rank correlation. How is it measured?. Write down the formula for coefficient of Rank correlation when there are ties. Q 20. The following are the marks obtained in statistics (x) and mathematics (y) of 10 students in B.com. Examination. Find the coefficient Rank correlation. X y
43 30
96 94
74 84
38 13
35 30
43 18
22 30
56 41
35 48
80 95
Q 21. (a) What is regression? Explain properties of regression lines. (b) prove that
(c) Find the regression coefficient
n=50also obtain two regression equations.
Q 22a) The following table gives marks of 6 students in Economics & Statistics. Estimate (1) Marks of students in Economics whose marks in statistics = 80 (2) Marks of student in statistics whose marks in econ omics = 50 S .NO.
1
ECONOMICS 62 STATISTICS
70
2
3
4
70
65
76
74
68
5
78
6 68 74
60 64
Q 23. (a) The regression lines of a bivariate populations are
Find the mean of X & Y series.
(b) From the following bivariate data identify the two regression eq uations. Also find
Q 24. (a) In a college 20% of students are girls. In a random sample of 5 students find the probability (i) 2 are girls
(ii) at least 3 girls.
(b) 5 fair coins are tossed 128 times. Write down theoretical frequencies o f the distribution of head. Q 25. (a) The probability that a razor blade manufacture by a firm is defective is
. Blades are
supplied in a packet of 5 each. In a lot of 10000 packets how many packets would be (i)Free of defective
(ii) contains exactly one defective blade?
Q 26. (a) Give two examples to each of the following. (i) Binomial variate (ii) Poisson variate (iii) Normal variate. (b) Write down the probability function, Mean, variance of each of Binomial, poisson and normal distributions. Q 27. Discuss why poisson distribution is widely used in statistics? Q 28. Give properties and importance of normal distribution. Q 29. The mean & SD of marks obtained by the candidates in a competitive examination are 50, 15 respectively. If 1200 candidates appear for the examination (a) Find the number of candidates who are expected to score more than 70 marks. (b) The expected number of candidates who score between 58 & 80 marks. Q 30. X is normal with mean 64 &variance 144. Find the probabilities that (i)
X 67 (2) 60 X 66
(3) X < 62.