problem 1)a) What do you know about frequency distribution and its significance. How do we construct it? 

b) For the purpose of performance evaluation and quota adjustment, Mr. Hanif monitored auto sales of his 40 salespeople. Over a 1-month period, he sold the following number of cars:

7       8     5   10    9    10     5    13    8    6
10    11    6    5    10    11    10   5     9    13
8      12    8    8    10    15    7    6     8     8
5       6     9    7    14    8      7    5     5    14

(i) Based on frequency, what would be the desired class marks (midpoints of the intervals)?

(ii) Create a frequency and relative frequency distribution having as many of these marks as possible. Make your intervals evenly spaced and at least two cars wide.

(iii) If sales fewer than seven cars a month are considered unacceptable performance, which of the two answers, (a) or (b), helps you more in identifying unsatisfactory group of salespeople?

problem 2)a) What do you mean by frequency Polygon and Ogives. How do we draw these?

b) For the following frequency distribution, find out:   

i) The median class.

ii) The width of the equal steps in median class.

iii) The estimated value of the median for these data.

Class              Frequency        Class           Frequency

100 – 149.5       12             300 – 349.5         72
150 – 199.5       14             350 – 399.5         63
200 – 249.5       27             400 – 449.5         36
250 – 299.5       58             450 – 499.5         18

problem 3)a)    State life Insurance provides information to its subscribers to allow them to evaluate performance of mutual funds they are considering as potential investment vehicles. A recent survey of funds whose stated investment goal was growth and income produced the following data on total annual rate of return over the past five years:

Annual return (%)    11.0 – 11.9    12.0 – 12.9    13.0 – 13.9    14.0 – 14.9    15.0 – 15.9    16.0 – 16.9    17.0 – 17.9    18.0 – 18.9
Frequency                       2                  2                    8                 10                  11                  8                  3                   1

i) Compute the mean, variance, and standard deviation of annual rate of return for this sample of 45 funds.

ii) According to Chebyshev’s theorem, between what values must at least 75 percent of the sample observations fall? What percentage of observations actually does fall in that interval?

iii) As the distribution is roughly bell-shaped, between what values would you expect to find 68 percent of observations? What percentage of observations actually does fall in that interval?

b) Students’ ages in regular daytime M.B.A. program and evening program of AIOU are described by these two samples:

Regular M.B.A    23    29    27    22    24    21    25    26    27    24
Evening M.B.A    27    34    30    29    28    30    34    35    28    29

If homogeneity of class is a positive factor in learning, use measure of relative variability to suggest which of the two groups will be easier to teach.

problem 4)a)    The engineer tested nine samples of each of three designs of a certain bearing for a new electrical winch. The following data are the number of hours it took for each bearing to fail when the winch motor was run continuously at maximum output, with a load on the winch equivalent to 1.9 times the intended capacity.

       Design

A       B    C
16    18    31
16    27    16
53    23    42
15    21    20
31    22    18
17    26    17
14    39    16
30    17    15
20    28    19

i) Compute the mean and median for each group.

ii) Based on your answer, which design is best and why?

b) Irfan Ahmad does statistical analyses for automobile racing team. Here are the fuel consumption figures in miles per gallon for the team’s cars in recent races:

4.77    6.11    6.11    5.05    5.99    4.91    527    6.01
5.75    4.89    6.05    5.22    6.02    5.23    6.11    5.02

i) Compute the mean and median fuel consumption.

ii) Group the data into five equally sized classes. What is the fuel consumption value of the modal class?

iii) Which of the three measures of central tendency is best for Irfan to use when he orders fuel? Describe.

problem 5)a)    How would you reply to following statement: “Variability is not important factor as even though the outcome is more uncertain, you still have equal chance of falling either above or below the median. Thus, on average, the outcome will be the same.”   

b) Sarsabz Seed Company sells three grades of Early White Sugar corn seed, distinguished according to the consistency of germination of the seeds. The state seed testing laboratory has a sample of each grade of seed and its test results on the number of seeds that germinated out packages of 100 are as follows.

Grade I (Regular)    88    91    92    89    79
Grade II (Extra)      87    92    88    90    92
Grade III (Super)    90    89    79    93    88

Does Company’s grading of its seed make sense?