I purposely chose the number of phone calls received and not phone calls made in order to avoid any possible bias, which might arise out of conscious and purposeful dialing of the phone. The observation collected was based on randomly taken data for 10 chosen days and the nature of this dataset is time series. The data was collected such that a single day’s call would not stimulate any received call for the following days. This was consciously done in order to avoid bias.
Median value corresponds to observation=(n+1)/2, again if the number of observation is odd then we choose the middle value after arranging the observations in increasing order. Whereas if we have even number of observations as we have here, we take the mean of the two middle observations and it yields the median.
The mean value of 13.7 calls (14 approx) is much more than what I expected. The busy schedule usually cuts down the number of phone calls to 10 per day. The average should have been somewhere around 10 or 11.
The standard deviation is usually used to find the spread of the distribution of the available data set; here the number of phone calls in 10 days. It can also be said that it is a measure of variability. Square root of variance gives standard deviation.
To find out whether the given data set follows normal distribution or not we plot the frequency as we may see that we do not get a symmetrical curve, so our inference is that the data do not follow Normal distribution.
As it can be observed that the obtained frequency curve is not symmetrical, and hence we infer that the distribution is not Normal because the Normal distribution is a continuous distribution whereas the number of phone calls in 10 days is off course a discrete variable. Hence the most likely distribution that might be used is the Poisson distribution.
Now we continue collecting the data on the number of phone calls for five more days. Our basic question in this context would be whether this changes the