Sampling Technique and Data Analysis

Question 1
a) The sampling technique used for obtaining the given data would be terms as convenience
sampling which is a non-probability based sampling technique. This is because the responses
have been collected from first 400 responders. No attempt has been made to randomly derive
the sample from population of interest. It is likely that there is bias in the responses thereby
adversely impacting the reliability of the results obtained.
b) The number of cards is a discrete variable since the given variable has a numerical value
which can only assume integer values. This is because number of cards cannot assume
decimal values and hence it is not continuous.
c) The requisite graphical technique to capture the given data is bar chart where for each
number of cards, the corresponding bars would indicate the number of respondents having
these many cards.
d) The requisite graphical summary of the given data is obtained from Excel and illustrated
below.
e) It is evident from the above graphical representation that the distribution of number of cards
seems to have a positive skew. This is because there are a small number of respondents who

have 6 cards which is little unexpected considering that 99% of the respondents have four or
less cards. Also, from the distribution, it is apparent that the most common number of cards
held is 3 which has the largest frequency in the given data.
Question 2
a) Asset liability ratio would be a continuous variable since the underlying values are numerical
and also can assume decimal values and not restricted to only integral values. The
operational variable is nominal since it is a categorical variable which does not assume
numerical value and also the responses are of the type that cannot be arranged in a naturally
occurring order.
b) The requisite histogram for Asset Liability Ratio is shown below.
The above histogram clearly highlights that the shape is not symmetric owing to skew being
present. As a result, the maximum frequency interval does not occur in the middle of the
histogram.

c) A column chart would be used to allow for comparison of Asset Liability Ratio for the closed
and still operational small businesses. This is clearly evident from the following graph
obtained from Excel.
d) The requisite measures of central tendency and dispersion for Asset Liability Ratio have been
computed using Excel and presented below.
e) From the above output, it is evident that there is a significant different between the asset
liability ratio of the operational and closed businesses. The now closed small businesses have
mean and median value of asset liability ratio of about 0.5 which would have been a major
reason for the closure of these businesses. This value implies that the corresponding assets
are significantly lower than the outstanding liabilities thereby indicating inability to meet the