Question

A researcher is interested to examine the impacts of the Covid-19 pandemic towards the waiting time of patients to see doctors in the general practitioner (GP) clinics. He recorded the waiting time (in minutes) of 33 randomly selected patients at various GP clinics in the inner city suburbs of Brisbane. After collecting the data, he used Excel to run the numerical descriptive analysis and produced the following outputs.  

Waiting Time (in minutes)  

Mean	28.4697
Standard Error	1.5784
Median	30
Mode	35
Standard Deviation	9.0674
Sample Variance	82.2178
Kurtosis	1.0567
Skewness	0.2673
Range	44
Minimum	10
Maximum	54
Sum	939.5
Count	33

Assist the researcher in interpreting the outputs by answering these questions.

a) Provide an interpretation of the reported value of the mean in the context of the problem.                  

b) Provide an interpretation of the reported value of the median in the context of the problem.                       

c) Provide an interpretation of the reported value of the first quartile in the context of the problem.                

d) If you were to draw the histogram of the data set, what shape of distribution do you think the data collected would resemble? Provide a brief justification to your answer.   

e) Calculate the approximate standard deviation using the relevant formula. Display working.   Provide a reason on why the approximate standard deviation you calculated differs substantially to the standard deviation value reported in the table.   

Answer 1

a. Interpretation of mean:
On an average a covid-19 patient has to wait 28.4697 minutes to see a doctor.

b. Interpretation of median:
50% of the time is where the covid-19 patients had to wait for the doctor is below 30 minutes and 50% of time where the covid-19 patients had to wait for the doctor is above 30 minutes

c. Interpretation of first quartile:
25% of the time is where the covid-19 patients had to wait for the doctor is below the first quartile value and 75% of time where the covid-19 patients had to wait for the doctor is above first quartile value

d. Since the skewness is positive here hence, the histogram is right skewed. Also the kurtosis is posistive so we can expect heavier tails near the edges of histogram.

Note: We are legally bound to solve only first four parts of the problem.

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