Can statistical probability distributions reveal CX operational challenges?

Statistical probability distributions might not be widely used due to their perceived complexity and mathematical nature in customer service centers. However, they hold immense importance because they provide a structured framework to understand and model uncertainties in real-world phenomena. Distributions offer insights into the likelihood of different outcomes, aiding decision-making, risk assessment, and resource allocation. They allow us to quantify and communicate uncertainty, enabling better-informed choices and effective problem-solving. Despite their initial complexity, grasping probability distributions empowers us to navigate uncertainty, make predictions, and drive more accurate and insightful analyses.

I have intentionally used a few simplified examples to explain 4 statistical distributions in MS Excel that have a huge relevance in driving customer experience operations. In real-world scenarios, data analysis might involve more sophisticated statistical models and larger datasets though.

Example 1: Response Time Analysis using Normal Distribution

Suppose a customer service center wants to analyze the response time of its customer support team to address customer inquiries. They have collected data on the response time for a sample of 50 customer inquiries over the past month.

• Let's assume the response times (in minutes) for the 50 inquiries are as follows:

15, 20, 10, 30, 25, 18, 22, 17, 28, 14, 12, 27, 16, 19, 23, 26, 21, 29, 24, 32,

35, 38, 36, 33, 31, 39, 40, 42, 37, 43, 44, 46, 48, 41, 50, 45, 47, 55, 53, 52,

54, 51, 49, 58, 57, 56, 59, 60, 61, 62, 63

• Open MS Excel and input the data into a spreadsheet. Let's assume the data is in column A, starting from cell A2 to A51

- First, calculate the mean of the response times:?=AVERAGE(A2:A51)

- Next, calculate the standard deviation of the response times:

=STDEV(A2:A51)

• Replace "mean_value" and "standard_deviation" with the respective cell references for the mean and standard deviation you calculated above.
• Now, you can use these values to calculate probabilities for different response time scenarios using the normal distribution function. For example, to find the probability that a customer inquiry will be addressed in less than 25 minutes, you can use the following formula:

=NORM.DIST(25, mean_value, standard_deviation, TRUE)

• Inference : This information can help the customer service center to understand the likelihood of responding to customer inquiries within specific time frames. They can set performance targets, identify potential outliers or bottlenecks, and make data-driven decisions to improve customer support efficiency and overall experience.

Example 2: Error Rate Analysis using Binomial Distribution

Suppose a customer service center wants to analyze the error rate in a sample of 100 interactions for a process. They want to calculate the probability of a certain number of defective interactions based on historical data.

• Let's assume the customer service center has historical data that suggests that the error rate for this process is 10%. They want to know the probability of finding a specific number of defective interactions in a sample of 100.
• Open MS Excel –

- In cell A1, write "Number of Defective Interactions"

- In cell A2, enter the numbers from 0 to 10 (representing the number of

defective interactions).

- In cell B1, write "Probability"

- In cell B2, enter the formula to calculate the binomial probability using

Excel's BINOM.DIST function: =BINOM.DIST(A2, 100, 0.1, FALSE)

• This formula calculates the probability of getting exactly the number of defective interactions specified in cell A2 out of a sample of 100, with an error rate of 10%.
• Inference : This information can help the customer service center to assess the potential error rates and plan quality control measures accordingly.

Example 3: Call Arrival Rate Analysis using Poisson Distribution

Suppose a customer service center receives an average of 20 customer calls per hour. The center wants to analyze the probability of receiving a specific number of calls in a given time period.

• Let's assume the company wants to calculate the probability of receiving a certain number of calls in a 1-hour period based on an average call arrival rate of 20 calls per hour.
• Open MS Excel –

- In cell A1, write "Number of Calls"

- In cell A2, enter the numbers from 0 to 40 (representing the number of calls)

- In cell B1, write "Probability"

- In cell B2, enter the formula to calculate the Poisson probability using Excel's

POISSON.DIST function: =POISSON.DIST(A2, 20, FALSE)

• This formula calculates the probability of receiving exactly the number of calls specified in cell A2 in a 1-hour period, given the average call arrival rate of 20 calls per hour.
• Inference : This information can help the customer service center to gain insights into call arrival patterns, estimate the likelihood of different call volumes, and make data-driven decisions to optimize staffing and resource allocation for better customer experience.

Example 4: Number of Attempts for a Successful Sale using Geometric Distribution

Suppose a sales team is analyzing how many attempts it takes, on average, to make a successful sale to a potential customer. Historical data suggests that the probability of making a sale on any given attempt is 10%.

• Open MS Excel –

- In cell A1, write "Number of Attempts"

- In cell A2, enter the numbers from 1 to 10 (representing the number of

attempts).

- In cell B1, write "Probability"

- In cell B2, enter the formula to calculate the geometric probability using

Excel's GEOMEAN function: = GEOMEAN (1-0.10, A2-1) * 0.10

• This formula calculates the probability of making a successful sale on the attempt specified in cell A2, given the 10% probability of success on any given attempt.
• Inference : This information can help the sales team to estimate the average number of attempts needed for a successful sale and can guide them in optimizing their sales strategies and making informed decisions to improve customer conversion rates.

When working with statistical distributions, exercise caution by ensuring data quality and being aware of assumptions and biases. Choose appropriate distributions based on data characteristics and consider the impact of outliers and non-random sampling. Be mindful of overfitting and the applicability of chosen models. Understand the context of results and differentiate between correlation and causation. Validate distribution fits and acknowledge the importance of sample size and parameter estimation in ensuring accurate analysis.