Suppose we want to take a poll of the attitudes of senior citizens in the State

Question

Suppose we want to take a poll of the attitudes of senior citizens in the State of Washington. Using this example, describe in your own words how you would go about determining this through:

a.       Drawing a random sample

b.      Drawing a systematic sample

c.       Drawing a convenience sample

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The “average” is a commonly reported statistic. This single bit of information can be very informative or very misleading, with the mean and median being the two most commonly reported.

The mean is a useful measure, but it can be misleading. Describe a circumstance when the mean is very useful as the average and a circumstance when the mean is very misleading as the average.

Explanation / Answer

a. Random Sampling: Random sampling consists of a set of individuals from the population chosen in such a way that every set of individuals has an equal chance of being the sample actually selected. This is often the best and most appropriate way to collect data for a sample.

For the current poll, every senior citizen can be assigned a unique number, say from 1 to 10,000 by searching from the social security database. Then use a random number generator to choose a set of 50 senior citizens among all the senior citizens who have been provided with a unique number. Then the poll can be conducted over the selected random sample of 50 senior citizens.

(b) Systematic Sampling: This method of sampling is conducted by randomly selecting an arbitrary starting point, and then select every kth member of the population. In the present case, a starting point can be selected, say the 50th member from the set of senior citizens with unique identification number. Then draw the sample by selecting every 50th member of the population to form sample and then conduct the poll among the selected sample of senior citizens.

(c) Convenience Sampling: This type of sampling uses subjects that are easily available. This type of sampling is the most biased. In the present problem, the sample can be selected by visiting an old-age home, or by visiting a relatively well-off locality of the state, etc. The poll can be conducted on the selected sample. The results are likely to be biased due to the presence of citizens with similar mindsets or citizens from the same social environment.

2. Mean usually refers to arithmetic mean. The mean provides very useful information in cases where the data is relatively symmetric. For example, if the data is nearly normally distributed, then the mean is the best measure of central tendency. However, if the data is very skewed and contains extreme values, then the arithmetic mean might become misleading.

Mean is very useful as the average when the data set have similar value, for example, the heights of students in a class, the distance travelled by a particular vehicle per litre of fuel, etc.

But the mean would be misleading in the following situation: Let's say there are 5 employees in a particluar department with salaries 18,000; 19,000; 20,000; 21,000 & 22,000. The average salary is 20,000. Then an expert joins the department with a salary of 200,000. Now the average salary of the department is 50,000. But this average is not a correct representation of the salary of the employees in the department.

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