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Math 130: Basic Statistics Question Paper
Math 130: Basic Statistics
Course:Agriculture And Natural Resource
Institution: Kenya Methodist University question papers
Exam Year:2012
Instructions: Answer Question ONE and any other TWO Questions.
SECTION A
Question One
a) Distinguish between descriptive and inferential statistics. (4 marks)
b) Consider the following data set.
X= {11, 13, 15, 16, 19, 22, 13, 20}. Calculate:
i. Arithmetic mean (3 marks)
ii. Harmonic mean (3 marks)
iii. Geometric mean (3 marks)
c) Determine the number of permutations of the letters of the word “HALLUCINATIONS” (3marks)
d) Five percent of all TVs manufactured by a large electronic company are defective; a quality control inspector randomly selected three TVs from the production line. What is the probability that exactly one of these three TVs is defective? ( 4 marks)
e) A committee consists of 20 persons. In how many ways can the members sit around a circular table so that the chairman sits between the secretary and the treasurer? (4marks)
f) The following is the distribution of marks of 230 students in a test.
marks % 10-20 20-30 30-40 40-50 50-60 60-70 70-80
frequency 12 30 35 65 45 25 18
Represent this s data by means of a histogram and use your histogram to estimate the mode of the distribution. (6 marks)
Question Two
The following data relates to annual profits in thousands of shillings made by an ICT firm in different years.
28 35 61 29 36 48 57 72
48 40 47 42 41 37 51 62
31 32 35 40 38 37 44 51
37 46 42 38 61 59 60 44
38 44 45 45 47 38 58 47
69 63 54 39 47 50 33 56
57 64
a) Taking 25-34, 35-44 etc as class intervals, construct a frequency distribution table for the data. (6 marks)
b) Construct an ogive and find the: (14 marks)
i. Number of firms having profit between shs 37,000 and shs 58,000.
ii. Profit above which 10% of the firms will have their profits.
iii. Median profit.
Question Three
a) The following sample observations were randomly selected.
x 4 5 3 6 10
y 4 6 5 7 7
i. Determine the regression equitation of the form y=ax + b to the data. (7 marks)
ii. Determine the value of y when x is 7. (3 marks)
b)
i. What is meant by correlations? (2 marks)
ii. Ten competitors in a beauty contest are ruled by 3 judges in the following order.
1st Judge 1 6 5 10 3 2 4 9 7 8
2nd
Judge 2 5 8 4 7 10 2 1 6 9
3rd
Judge 3 4 9 8 1 2 3 10 5 7
Use the rank correlation coefficient to determine which pair of judges has the nearest approach to common tastes in beauty. (8 marks)
Question Four
a) Distinguish between skewness and kurtosis. (2 marks)
b) Using a clearly labeled diagram, show the passion of mode, mean and median of a negatively skewed distribution. (3 marks)
c) The following is the distribution of weights of 140 fresher’s joining a university.
Weight (pounds) Frequency
80-89 4
90-99 23
100-109 49
110-119 38
120-129 17
130-139 6
140-149 3
Calculate the median weight and the standard deviation, hence compute thee Karl Pearson’s coefficient of skewness and interpret it (15 marks)
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