A set or group of values relating to qualitative or quantitative variables is known as data. Data usually gives information on the business, its people, objects and places. Every business deals with data and a lot of data are generated from the businesses. The data generated by these business firms can be analyzed to improve the business quality. Based on the analysis results, the managers can understand their areas of development to further increase the business. In this study, the data on call centres will be analyzed.
The data on the call centre was collected as a result of a survey on a call centre having operations in Dublin, Cork and Galway. 50 Staffs were randomly selected from these centres and their performances were strictly measured for 1 hour. They were monitored on three different grounds, the number of phone calls taken in an hour, the duration of phone calls taken, and the category of the phone calls.
Here the analysis will be performed on the two variables, Number of phone calls taken in an hour and duration of the phone calls. Here Number of phone calls is our discrete variable and the duration of phone calls is our continuous variable. The required analysis and interpretations are done in the following sections.
The telecalling companies give several targets to their employees of attending the minimum number of calls. For example, let the target for the number of calls per day be 60. A telecaller should not make too many calls exceeding 60. Making too many calls will show that the caller is not making any productive calls. Many calls are useless and the caller cannot convince the customer. Thus they are making calls of shorter duration hence resulting in more calls. This might be bad for the employee. Again, if a caller makes calls with longer duration, this might mean that the particular caller will not be able to meet the daily target of 60 calls. All his calls are of longer duration and making 60 calls will not be possible within the shift time. This will share the message that this particular employee is taking too long time to convince or explain a certain thing to the customers. This will put a negative impact on the telecaller and his job may be in jeopardy (Levitan 2013).
A variable taking only countable number of values is known as a discrete variable. Now, if the sum of the probabilities of the values of a variable is equal to 1, then the variable is a random variable. A continuous random variable on the other hand can take infinitely many values. According to the definitions stated, the variable number of phone calls in an hour is a discrete random variable and the duration of phone calls is a discrete random variable.
The mean of the data recorded against each employee for number of phone calls in a day and duration of phone calls is necessary. This will show whether the employee is able to meet the target or not on an average. Median is the kind of measure that shows the middlemost point of a distribution. The median will also help to understand the mid value of the number of calls the caller takes, or the duration of calls the caller takes. The equality of mean and the median will indicate that the data is symmetric. This means that the number of calls above and below the mean are equal. If mean is more than the median, then the data is negatively skewed (Results shown in table 2 in appendix). This means more calls are of long durations or callers are taking calls more than the mean number of calls. This analysis will also help to reduce the waiting time of the customers when they are calling the customer service, by analyzing the duration of calls (Giambene 2014).
To understand and conduct this study, data has been collected on the average number of calls attended by a caller in an hour, and the duration of calls. The data on duration of phone calls contains 10 samples. From those 10 samples, the mean of the call durations has been calculated. The normal probability plot has been done by using the mean of the call durations. The data is a continuous data. The descriptive statistics measures for the data has been calculated. The mean of the data is very close to the median. Thus, the data can be said to be symmetric. Again for the measures of dispersion, Standard deviation and range of the distribution are calculated. The range of the distribution is small. It can be said that the data points are not much scattered, they are close to each other. The standard deviation is also very less. This shows that the data points are very close to the mean of the data (Levine, Berenson and Stephan 2014). The normal probability plot for the data of 50 sample telecallers is shown by the following figure (Herkenhoff and Fogli 2013).
Let t be a time within which n events has to be occurred. This can be stated with an example of the number of misprints in each page of a book. The events are independent. Occurrence of one event does not depend on the occurrence of the other. These types of events are said to follow Poisson distribution having a probability mass function
f(x) = , with mean of the distribution as λ.
The number of phone calls received in an hour, is a discrete data and follows a Poisson distribution (Meeker, Hahn and Escobar 2017). With the formula for probability mass function, the probability for any number of phone calls in a day can be estimated. The Poisson probability plot for the data is shown in the following diagram (Abbott 2014). The table for the probability plot is given in table 1 in the appendix section.
The most commonly used distribution in statistics is the normal distribution. The reasons for which the normal distribution is the most important distribution is that, it most of the business variables closely resemble the normal distribution. Various discrete distributions can be approximated to normal distribution. The normal distribution has the following properties:
The probability density function of the normal distribution is given by:
f(x) = , where -∞ ≤ x ≤ ∞
µ and σ are the mean and variances of the distribution (Levine, Berenson and Stephan 2014).
In general, the sample distributions are not always normal distributions. In fact in most of the cases, sample distributions are not normal distributions. These follow different distributions such as student’s t, F, T, Chi Square, Z distributions. With the increase in the sample size, all these distributions can be approximated to normal distributions. Thus, normal distribution are assumed for sampling distributions (Hogg, Tanis and Zimmerman 2014).
Inferential statistics is mainly used to draw an inference about the population by studying a part of the population, that is, a sample of the population. Moreover, inferential statistics is used to make a decision of the probability whether an observed difference within a group is dependable or not. Most of the times a Bivariate or multivariate analysis is helpful in inferential statistics. Inferential statistics can be used to compare the distribution of the sample data. It can also be used to test the rule of central limit theorem.
In this study, the continuous variable chosen is the duration of phone calls. Every company in today’s market has a telecom sector. They are there to help the customers solve their problems or answer their queries. Thus, for the telecom departments of the companies, it is important to record the number of phone calls attended per day. The duration of each call is also important to note. These will help the companies to understand the capability of each member of staff to take calls each day. According to this analysis they can decide on the number of employees they need to hire by minimizing the cost. The duration of 10 sample phone calls taken by 50 members or staffs of a company are given in the data. This has been analyzed using appropriate statistical technique.
Inferential statistics are of two types – Point estimation and Interval Estimation (Hogg, Tanis and Zimmerman 2014).
Confidence Interval is a type of interval estimation. Confidence interval is used to explain the percentage or amount of uncertainty associated with an estimate of the sample to infer about the population. A 95% confidence interval states that there is 95% chance that the interval covers the whole population. Confidence interval gives a range of values which will be a good estimator of the unknown population parameter. Since the observed data is a random sample, the confidence interval so obtained will also be random. A 95% confidence interval indicates a 0.05 level of significance. Similarly 90% and 99% confidence intervals are also used according to the needs of the studies (Kisbu-Sakarya, MacKinnon and Mio?evi? 2014).
The confidence interval of a normal distribution with mean µ and variance is given by (±1.96), is the sample mean, σ is the sample variance and n is the sample size. The population mean is estimated to lie between this interval. If the population mean lies between this interval, the null hypothesis will be accepted, otherwise it will be rejected (Levine, Berenson and Stephan 2014). In this analysis, the confidence interval is (5.493, 5.494). The values of the population are expected to lie within this interval with a chance of 95%. In the context of this study, there is a 95% chance that the average duration of calls lies between 5.493 minutes to 5.494 minutes.
Conclusion
From the study above, it is evident that the number of phone calls in an hour should be around 7. More than 7 calls or less than 7 calls in one hour might put a negative impact on the employee. Again, the duration of phone calls is most likely to be 5.49 minutes. This way both the recruiters and the employees are satisfied. The probability distribution assumed for the duration of phone calls to follow was normal distribution. From the study, it was seen that the data is also symmetric. Thus, it can be said that the analysis supports the assumption.
References
Abbott, M.L., 2014. Understanding educational statistics using Microsoft Excel and SPSS. John Wiley & Sons.
Giambene, G., 2014. Queuing theory and telecommunications: networks and applications. Springer Science & Business Media.
Herkenhoff, L. and Fogli, J., 2013. Applied statistics for business and management using Microsoft Excel. Springer Science & Business Media.
Hogg, R.V., Tanis, E. and Zimmerman, D., 2014. Probability and statistical inference. Pearson Higher Ed.
Kisbu-Sakarya, Y., MacKinnon, D.P. and Mio?evi?, M., 2014. The distribution of the product explains normal theory mediation confidence interval estimation. Multivariate behavioral research, 49(3), pp.261-268.
Levine, D.M., Berenson, M.L. and Stephan, D., 2014. Statistics for managers using Microsoft Excel (Vol. 660). Upper Saddle River, NJ: Prentice Hall.
Levitan, G., Virtel Corporation, 2013. Integrated virtual telecommunication system for E-commerce. U.S. Patent 5,864,823.
Meeker, W.Q., Hahn, G.J. and Escobar, L.A., 2017. Bayesian Statistical Intervals for the Binomial, Poisson, and Normal Distributions. Statistical Intervals: A Guide for Practitioners and Researchers, pp.325-350.
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