SSC201_Theory_Questions.txt

[MAX]37[/MAX] [QUESTIONS] What do you understand by the term 'Statistics'? A sample may be preferred to a population in statistical enquiry. State two reasons in favour or against the statement. Mention two shortcomings of Stratified sampling technique. Calculate the median, variance and mean deviation of 6, 8, 14, 10, 16 and 18. List three national/international agencies that do publish data and name one publication each of them publishes. What is a Sampling Frame? State the relationship between the mean, median and mode of a negatively skewed frequency distribution. Name one instrument for collecting primary data. If the sum of twelve (12) scores is given as (245 + K) while the mean is 26. What is the value of K? (K is a constant) Highlight three main characteristics of a good Table. State two conditions required under Inferential Statistics. What is Ratio? What are Quantiles? The score below show the marks obtained by a particular department out of many that participated in ECN401 examination in 1985/86 session

52 40 68 58 78 63 42 53 45 58
70 60 65 50 58 53 70 50 53 68
53 62 50 45 63 55 62 50 47 50
28 43 55 58 78 40 63 57 57 65
70 23 45 43 67 53 83 52 43 53
72 73 42 40 40 17 78 10 27 48

Use the data to:

a. Construct an absolute, a cumulative and a relative frequency distribution tables using a class's width of 10.

b. Estimate the mode, median and mean of the distribution.

c. If an assumed mean of 53 is used, what will the mean he?

d. Calculate the range, variance, 6th decile, 70th percentile and the 3rd quartile.

e. Draw a histogram and frequency polygon of the distribution.

f. Find the coefficient of skewness for the data and interpret your result.

g. If a candidate scored 57 in the examination, did he perform satisfactorily?

h. Draw an ogive and use it to determine the number of students that scored above the 3rd quartile. a. What is a random variable?

b. Find the probabilities of the following, given that the mean and variance are 8 and 49 respectively:
(i.) x > 30.
(ii.) -12 < x <21.
(iii.) x < -2.19.

c. Mention five key steps in hypothesis testing.

d. Draw a well labeled diagram showing the acceptance region and rejection region. A term of medical experts assessing the effects of Avain flu has assured the public that the probability of getting infected among humans is only 0.06. Five hundred people living in the affected states are selected for study. What is the probability that;

i. None of them is having the disease.
ii. Exactly four of them are having the disease.
iii. At least four of them are having the disease.
iv. At most three of them are having the disease. a. A random sample of 300 students indicate that their weights are normally distributed with mean 68kg and variance 9kg. How many students have weights.

i. Greater than 72kg.
ii. Less than 64kg.
iii. Between 65kg and 71kg.
iv. Greater than 68kg.

b. In a perfectly competitive market, the probability that a firm will close down it's operations is 0.35. Suppose 10 firms are selected at random. What is the probability of:

i. at least two firms closing down.
ii. exactly four of them closing down.
iii. at least two firms that are not closing down. Give two reasons why sample is preferred to population. Calculate the harmonic mean and mean absolute deviation of the set of data 6, 8, 14, 10, 16 and 18 List three national and international agencies that do publish data and name one publication each of them publishes. A student's grade in the statistics test 1, 2 and 3 are 71, 78 and 89 respectively. If the weights accorded these grades are 2, 4 and 5. What is the appropriate average grade of the students? Obtain the root mean square deviation of the numbers 11, 23 and 35. Given that the sum of nine scores is (80 + N) while their mean is 14. What is the value of N? Define the term hypothesis testing. Distinguish between type 1 error and type 2 error. The weight to the nearest Kg of a group of students in a course is given as follows:

65, 70, 60, 46, 51, 55, 59, 63, 68, 53,
47, 53, 72, 53, 67, 62, 64, 70, 57, 56,
73, 56, 48, 51, 58, 63, 65, 62, 49, 64,
53, 59, 63, 50, 48, 72, 67, 56, 61, 64,
66, 52, 49, 62, 71, 58, 53, 69, 63, 59

(a). Using assumed mean of 62, calculate the mean and standard deviation of the grouped data.

(b). The following data represents the commuting times in minutes for different employees at a local store: 19, 21, 14, 25, 21 and 20. Find the basic measures of central tendency and dispersion.

(c). From (b) above, if on a certain day, due to an accident, each employee takes an additional 5 minutes to commute to work. What would be the new mean, median, mode, range and standard deviation for that day? Explain your answer.

(d). Given the following set of data 8, 3, 9, 5, 43, 10. Identify the outlier for the data set and in what ways do you think elimination of the outlier affects the measures of dispersion. (a) The probability two independent companies Y and Z will survive in the next five years are 0.75 and 0.80 respectively. Calculate the probabilities that in the next five years:

i. both companies will survive.
ii. one of them will survive.
iii. none of them will survive.

(b) Two dice are tossed at the same time in an experiment. Find the probabilities of getting:

i. the sum of numbers divisible by three.
ii. the sum of numbers less than seven.
iii. same faces.

(c) With the aid of appropriate example, clearly distinguish between mutually exclusive events and independent events. (a) In a family of four children, the probability that a child is a boy or girl is equally likely. Given that x is the number of boys, obtain:

(i) the distribution of x.
(ii) the expected value and variance of x.
(iii)assuming there are 2000 families, find the expected value of x = 0 and x = 2.

(b) Suppose the number of a company employee who are absent on Monday have approximately a Poisson distribution. Furthermore, assuming that the average number of Monday absentees is 2.6, find:

(i) the mean and standard deviation of the number of employees.
(ii) the probability that at most two employees are absent on a given Monday.
(iii) the probability that more than five employees are absent on a given Monday.

(c). The mean score of students in an examination is 50, while the standard deviation is 100. What percentage of the students do we expect to score above 80? Highlight four methods of data presentation in statistics. List two advantages and two disadvantages of using sample for a survey. Find the mean number of heads in 100 tosses of a coin. The geometric mean of 7, 10, 6, 12, 6, 5 and 3 is? a. Differentiate between measures of central tendency and measures of dispersion.

b. The scores of 60 students in a SSC201 examination were given as follows:

7 19 20 21 24 37 13 20 0 21
10 31 22 28 36 18 12 23 19 18
23 25 35 23 27 25 20 40 19 16
11 30 21 15 19 24 22 18 26 13
21 19 41 19 14 27 16 17 9 8
29 26 19 16 22 29 21 21 4 5

Using the sample size of 5, calculate the:
<(i) Mean
(ii) Median
(iii) Mode.

c. Compute the
(i) Mean Absolute Deviation
(ii) The difference between the Standard Deviation and Mean Absolute Deviation a. Explain each of the following concepts and give appropriate example
(i) Harmonic Mean
(ii) Mode
(iii) Variance
(iv) Mean Absolute Deviation
(v) Quartile Deviation

b. State 3 properties of Arithmetic mean and 2 properties of Range.

c. In 2014/2015 Mid-semester test in SSC201 at OAU, Ile-Ife, 4 students scored 10 marks, 9 students scored 24 marks, 11 students scored 20 marks, 7 students scored 27 marks and 9 students scored 33 marks. Find the mean and the mode scores of the distribution. a. Distinguish between the following terms.

(i) Random experiment and sample space
(ii) Mutually exclusive and independent events.

b. The probabilities that John and Frank will pass their examination are 1/3 and 2/5 respectively. Calculate the probability that:

i) both of them would pass
ii) only John would pass
iii) either of them would pass
iv) neither of them would pass
v) at least one of them would pass

c. A class contains 25 students from Demography Department and 35 students from Economics Department. Two students are randomly selected from each class "without replacement". Find the probability that:

i) they are both from Demography department.
ii) they are from different departments. a. Distinguish clearly between simple bar chart and histogram.

b. The data collected by a teacher on the score of 50 students in a statistics test are as follows:

58 15 81 79 92 58 69 32 45 56
41 85 43 52 61 75 85 69 56 49
57 87 89 49 85 45 69 75 65 61
25 72 67 58 84 60 32 57 69 68
73 42 65 55 74 58 36 78 68 79

Hint: Using class interval of 11-20, 21-30...

(i) obtain the frequency table of the above data.
(ii) draw the histogram of the distribution and depict the frequency polygon on it.
(iii) Plot the cumulative frequency curve of the distribution. The difference between the following concepts with examples: Parameter and Statistic Descriptive and Inferential statistics [/QUESTIONS]