Analysis Of Call Data

Lower Quartile, Median, and Outliers

We recently implemented a new phone system that captures data on all incoming calls. The only automated report it produces looks like the image below. Can you tell me what each of the numbers mean? 

The lower quartile is 46 while the median (middle quartile) is 52. Upper quartile is 61 while the upper whisker is 69.

1. I searched Google to try and understand the above plot and it looked like it was left-skewed. Am I correct? What does this actually mean?

No the plot shows that the data is right-skewed. The plot means that the median number of daily incoming calls is lower than the mean daily incoming calls.

1. From searching Google about the above plot, it also looks like we only got two calls one day, but the quietest day I can remember in the last few months was around 35 calls. What could have happened here to get that number?

The number 2 is definitely an outlier. This could be as a result of wrong entry.

1. The system produces day-to-day totals, which are in the CallNumbers sheet, which was used to generate the above box-plot. Is this “2” an “outlier”? Are any others? Can you give statistical evidence that it’s an outlier? If so, I can use these to raise an issue with the phone system provider… Call Survey

Yes the “2” is an outlier as can be seen from the plot. There are other outliers for instance “69” is also an outlier. The given values are outliers since they are beyond the lower and the upper bounds. Any value beyond or below the upper and lower bound respectively qualifies to be an outlier.

1. My reception team has been following up every job we do. They have collected data on customer satisfaction for customers who are willing to participate in a short survey. The data are in the CallSurvey sheet. Can you please tell me the mean and standard deviation customer satisfaction rating (1-5)?

Solution

As can be seen from the above table, the mean satisfaction rating is 3.880 with a standard deviation of 1.202.

1. Can I please see a chart that compares the average satisfaction rating for each job type?

Emergency job type had a much higher satisfaction among the job types followed by maintenance while improvements had lowest satisfaction rating.

1. I’m interested in how many survey responses we got for each job type. Can you give me the AVERAGE TYPE of call? [Note from Adam: The average type of call is not possible. Please explain to Walter why we can’t do this and provide some numbers to answer his real question.] Call durations

It is not possible to get the average type of call since type of call is a nominal variable and not a numerical variable. Average can only be obtained for numerical variables. The only thing we can find is the count for each job type and not average. The count for each job type is given in the table below.

I want to know if our call durations have improved over the last few years. Our previous accounting firm generated the following chart in 2015 for our Annual General Meeting, but we don’t have the raw data anymore. Can you please approximate the mean and standard deviation for the call times from the chart?

Yes it is possible to estimate the mean and the standard deviation. The estimates are given as follows;

 We just started capturing call-duration data in the last few days. This is in the CallLog sheet. Can you please also calculate the mean and standard deviation for this sample of recent calls in the CallLog sheet?

Solution

As can be seen from the above table, the mean call-duration in the last few days is 4.499 with a standard deviation of 1.069.

1. Can you please let me know how these differ from the 2015 call durations and what might have changed in the business to cause the difference? Customer Ratings on Facebook

Solution

Job Satisfaction

The mean call time in 2015 was found to be 4.9913 with a standard deviation of 2.3157. The 2015 figures are slightly higher than the recent figures where the mean call time was computed to be 4.499 with a standard deviation of 1.069. This shows an improvement in the call durations over the last few years. What might have caused the difference is the management desire to improve on the call duration hence leading to the lower call duration.

We’re considering allowing customers to rate our service on our Facebook page. Based on the data from the CallSurvey sheet, can you tell me the probability of receiving a five-star rating? [Note from Adam: I’ve put together a contingency table and pasted it below to help you with this.]

Solution

I really need our Facebook ratings to be either 4 or 5 stars. Can you tell me the probability that jobs classified as “Improvements” will be rated LESS than 4 stars?

Solution

I want to include an average of Facebook ratings in our advertising. I’m thinking of only inviting customers to rate us on Facebook the job was an emergency or maintenance so the “Improvements” customers don’t bring down average our rating score. What do you think? Confidence in Satisfaction Scores

Solution

We compute the 95% Confidence Interval (C.I) as follows;

From the previous results, the average satisfaction score for the improvement job type was found to be 3.03. The 95% confident interval is between 3.6412 and 4.1188 and as can be seen the value of 3.03 is actually lower than the confidence interval for the overall satisfaction rating. Based on this, it would therefore not be a bad idea to only invite customers to rate us on Facebook given that the job was an Emergency or Maintenance in order to not allow the “Improvements” rating bring down average our rating score.

1. I am aware that the customer ratings collected in the CallSurvey sheet are just for a sample of three typical days and so the actual customer satisfaction could be slightly different if we had a bigger sample. How can I know this data in CallSurvey is reliable? Can you provide some information to give me 95% confidence in the overall satisfaction score?

Solution

To check how reliable the data is, we need to know the population average score and check whether the sample average confidence interval falls in the population average. To calculate the confidence interval we apply the following prcedures;

Confidence Interval (C.I) is given as;

So we are 95% confident that the true overall satisfaction score is between 3.6412 and 4.1188.

1. I also want to know how reliable the differences are in satisfaction scores between job type. Can you provide some information to give me 95% confidence in the satisfaction score for each job type?

Solution

95% confidence interval for difference in mean between Emergency and Improvements

Results

95% confidence interval for difference in mean between Emergency and Maintenance

Results

95% confidence interval for difference in mean between Improvements and Maintenance

Results

Based on the last question, is the satisfaction score between each job type really that different? How do you know? Changing Business Mix

Solution

Yes the above results shows that the satisfaction score between each job type are indeed significantly different.

The satisfaction scores are significantly different for Emergency and Improvements. The satisfaction scores were also significantly different for Emergency and Maintenance. The same was for Improvements and Maintenance.

1. The “Improvements” jobs have always been difficult. Customers usually get several quotes and we must be very competitive on price. It often en******** cost********s more than we expected. I’m wondering if we should stop trying to offer home improvement plumbing work and just focus on growing the “emergencies” side of the business. I’ve calculated the basic return on investment (ROI) for each of the jobs in the CallLog sheet. Based on that data, can you tell me if the ROI for the “Emergencies” job type is really lower than the ROI of the “Improvements” job type?

Solution

For this question, I sought to test the following hypothesis;

I tested this using t-test assuming equal variances at 5% level of significance. The results of the t-test are provided below;

As can be seen, the p-value for one-tail is 0.091 (a value greater than 5% level of significance), we thus fail to reject the null hypothesis and conclude that there is no significant evidence to say that the ROI for the “Emergencies” job type is really lower than the ROI of the “Improvements” job type.

1. I tried to work out the above question on my own. After some web searches, I got very confused. Can you give me a very brief explanation of what the null hypothesis is and whether it was accepted in the above answer?

Solution

The null hypothesis for the above question is;

 This null hypothesis was accepted since the p-value was found to be greater than 5% level of significance.

1. If this sample data shows a difference in ROI between the “Emergencies” and “Improvements” job types, what is the probability of your statistical test being incorrect? What type of error is this called?

Solution

The probability of the statistical test being incorrect is 0.909. This type of error is called Type II error-where we fail to reject the null hypothesis when in fact the alternate hypothesis is true.

1. What are your thoughts on changing the business mix to do more “Emergencies” jobs and fewer “Improvements” jobs?

Solution

In relation to the satisfaction rating, we established that Improvements job type had a much lower satisfaction score rating as compared to the Emergency job type.

However, the average return on investment (ROI) for the Emergency job type (M = 0.0756) was found to be lower than that of the Improvement job type (M = 0.2151).

It is important to note that every business would want to maximize on the ROI-in fact no business would prefer a business with a lower ROI. Based on the above findings, it would not be advisable to change the business mix by doing more “Emergencies” jobs and fewer “Improvements” jobs. My advice to Walter would be for him to look for other ways of improving the satisfaction rating for the Improvements job type rather than doing more of Emergencies and less of Improvements. Improvements will generate for him more ROI as compared the Emergencies.

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