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Meanwhile, the histograms and relative frequency distributions of the number of orders for each of the four quarters reflect all uni-modal distributions. There were, however, changes in the skewness of the distributions from the third quarter of 1990 to the second quarter of 1991. The third quarter distribution is negatively skewed, which illustrates that orders are more concentrated on the right side of the mean. However, the fourth quarter presented a positively skewed distribution suggesting that orders are more concentrated on the left side of the mean. The first and second quarters of the following year showed another shift towards a negatively skewed distribution. This reflects seasonality. Since the third quarter constitutes the end part of spring and halfway through summer when the weather is ideal for construction and repair projects, there was an observed increase in the number of orders. The change in skewness going towards the fourth quarter simply illustrates that there was a lesser number of orders since summer is past.
The histograms also confirmed the trend observed by Laurel that the customers of HH industries are increasing based on the low points of the histogram on the left slowly developing to higher points towards the right. Moreover, the tendency of the histograms to be negatively skewed points toward Laurel’s trending observation that orders will be more frequent. There is no confirmation yet from the histograms and relative frequency distributions that the orders are for smaller amounts than before since the available data is fluctuating from the 3rd quarter going to the 2nd quarter.
Based on the figures from Table 2.1 and Table 2.2, Laura’s intuitive findings from the histograms are supported. Seasonality is shown from the declining mean of the average order size during the first and second quarters and the corresponding high mean for the third quarter which falls mostly during summer. More frequent orders of smaller amounts are also verified based on the increasing mean of the total order and the decreasing mean of the average order size.
As to which measure of central tendency is most appropriate for the data at hand, I believe it is the median. The median is a value that represents a point below which half of all the data falls and above which the other half of data falls when the data are arranged in numerical order. When the median is used as a measure of central tendency for the total orders, Stan’s assumption that the total sales are doing would have been correct, since if the median of the total orders from Quarter 3 to Quarter 2 is plotted on a line graph, the trend would have been steadily increasing. However, this is only true for the total orders because the median of the average order size is also fluctuating.
As far as the actual figures on the total sales are concerned, Stan might not be correct. The total sales posted their peak for the fiscal year during the third quarter and took a 10.47% fall in the fourth quarter. Although total sales increased during the first quarter compared to the previous quarter (an increase was 1.40% of the fourth quarter sales), total sales in this quarter were still 9.22% lower than the third quarter. Total sales in the second quarter did not recover from the slump from quarter 3 total sales since total sales in the second quarter is 7.73% lower than the peak posted during the third quarter.
The warehouse exhibited a slightly different trend compared with the entire company in terms of the mean in total orders, where the warehouse or Profit Center 3 showed a steady increase, whereas the total orders for the entire company fell during the first quarter of 1991, represented in the chart by the number 3 in the x-axis. This revelation justifies Laurel’s planned investigation of the performance of each profit center as a good idea.
There was one data in the set from the third quarter which seemed to be very different from the rest. That value was in the seventh row under the Sales 1 column of Table 1 (191191). This sales data was the only one which reached the hundred thousand level. At first, I even thought that this was a typographical error. However, sales in this amount are not impossible so I continued with the computations.
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