Question

1. Consider a survey in which customers’ perceptions of the service at a local store are gathered using a Likert Scale. Using this survey the customer gives a score of 1, 2, 3, 4 or 5 in response to a statement about the service.

The scores represent

1 – Strongly Disagree

2 – Disagree

3 – Unsure

4 – Agree

5 – Strongly agree

For example, one of the statements might be “The staff member appears knowledgeable regarding the store’s products” and the customer would give a score based upon how much they agree with the statement. Now consider a situation in which 100 customers provide a response to this statement and they are distributed as follows

1 – Strongly Disagree 10 (10%)

2 – Disagree 25 (25%)

3 – Unsure 17 (17%)

4 – Agree 32 (32%)

5 – Strongly agree 16 (16%)

Now let’s assume that the store wants to summarise this data into a single score. They calculate this score by multiplying the number of responses by the number assigned, adding the five together and dividing by the number of respondents. In this case, (10 + 50 + 51 + 128 + 80) / 100 = 319/100 = 3.19

Explain why this value is not a valid summary of the data collected. Suggest a more valid way of representing the data. Justify your response.

Answer 1

The data which has been provided is a categorical data and calculating the mean of categorical data is not a valid summary of the data collected .What should be a more reliable and logical approach is to calculate a five number summary of observations which consist of the minimum,first quartile ,median,third quartile and the maximum of all observations. The values of these are given below:

We make the following table

Scores	Percentage	Cumulative Percentage
1	10	10
2	25	35
3	17	52
4	32	84
5	16	100

Min 1Q Median 3Q Max

1 2 3 4 5

This is a more valid way of representing the day since it does not involve the qualitative variable represented quantitatively into the summary formula.