Statistics I TU Board 2080 question paper

What do you understand by measures of central tendency and dispersion in descriptive statistics? What are the different measures of dispersion? The grouped frequency distribution in the table represents masses of a sample of 50 of the people from the data file, "Brain size".

Mass(lbs)
1-2
2-3
3-4
4-5
5-6
6-7
Frequency
8
10
15
9
6
2

Compute mean, standard deviation, variance and coefficient of variation and interpret them.

Discuss the meaning of i. positive ii. negative iii. perfect correlation between two variables. The following show the improvement (gain in reading speed) of 8 students in a speed reading program and the number of weeks they have been in program.

Number of weeks
4
5
3
9
7
10
4
5
Speed gain
85
120
48
192
164
234
74
110

• a) Compute correlation coefficient and interpret its result.

• b) Find the regression equation of speed gain on number of weeks.

• c) Estimate speed gain of a student who has been in program for 6 weeks and interpret the slope of the line.

The joint density function of two continuous random variables X and Y is

f(x,y)=kxy 0<x<4 , 1<y<5

=0 otherwise

• a) Find the value of constant k.

• b) Find P(x>3,y<2)

• c) Find P(1<x<2 , 2<y<3)

Differentiate between primary data and secondary data. What are the sources of secondary data?

What is sampling? Define simple random sampling and stratified random sampling with some relevant examples.

What aspect of summary measures of data can be explained by the measures of skewness? Kelvin Hota is the national sales manager for National Text Books. He has a sales staff of 10 who visit college professors all over the United States. Each Sunday morning he requires his sales staffs to send him a report. Listed below are the number of visits last week.

25, 6, 10, 13, 15, 2, 18, 5, 20, 30

Compute the five number summary.

What are the requisites for good average? From the following distribution of marks 200 students of a college:

Marks
30-40
40-50
50-60
60-70
70-80
80-90
No. of students
14
50
60
45
20
11

Compute:

• i) The minimum marks obtained by top 10% students.

• ii) modal marks.

The first four moments of a distribution about x=2 are 1,2.5,5.5 and 16. Calculate the first four moments about the mean. Test the skewness and kurtosis. Interpret the results.

Define independent and mutually exclusive events. Three groups of children 2 boys and 2 girls, 3 boys and 1 girl, 1 boy and 3 girls respectively. One child is selected at random from each group. Find the probability of selecting one boy and two girls.

What is conditional probability? Three roads A, B and C lead away from a jail. A prisoner escaping from the jail selects a road at random. If road A is selected, the probability of escaping is 1/10. Similarly for road B it is 1/8 and for road C it is 1/5.

• i) What is the probability that the prisoner will succeed in escaping?

• ii) If the prisoner has succeeded in escaping, what is the probability that he had chosen the road A?

Define binomial distribution. Under what conditions is the binomial distribution appropriate? The probability of a novice archer hitting the target with any shot is 0.3. Given that the archer shoots six arrows, find the probability that the target is hit at least once.

State features of normal distribution. In a photographic process, the developing time of prints as a random variable having normal distribution with mean of 18.25 seconds with standard deviation 0.34 seconds. Find the probability that at least 17.64 seconds to develop one of the prints.

Define random variable. If X is the number of points rolled with a balanced die, find E(X) and variance of X. Also find the expected value of random variable g(Y)=2X²+1.