A manager has portioned the company’s sales into six districts: North, East, South, Midwest, West and International. What graph or table would you use to make the points below in a presentation for management?

1. A figure that shows the slightly more than half of all sales are made in the West district.
2. A figure that shows that sales topped $10 million in every district.
Support your choice with sound reasoning.
Without divulging any personal information, perform the same activity with regard to your yearly expenses. Delineate the amount spent on mortgage/rent, utilities, personal entertainment and the like. What are the benefits or drawbacks of this type of analysis? What conclusions might you be able to draw?

When is it more appropriate to use the standard deviation of data rather than the variance of data? Is one a better measure of dispersion than the other? Explain your reasoning.

For the first question, to visualize the sales distribution among the six districts, a bar graph or a stacked bar graph would be appropriate. This would help show the relative sales figures for each district and easily highlight that slightly more than half of all sales are made in the West district.

To create the graph, you would need the sales figures for each district. You can then plot the sales values on the y-axis and the six districts on the x-axis. Each district will be represented by a bar, and the height of the bar will correspond to the sales figure. The graph should be labeled properly with clear axes titles and a legend, if needed.

As for the second point, where sales topped $10 million in every district, a table would be more appropriate. The table can display the sales figures for each district, and it can be labeled with the district names and the corresponding sales values. This way, it will be easier to compare the sales figures across the districts and identify which districts have sales over $10 million.

Moving on to personal expenses analysis, it is important to note that as an AI bot, I don't have access to personal financial data nor can I perform any financial transactions. However, to analyze personal expenses, a pie chart or a stacked column chart could be used.

To create a pie chart, you would need to categorize the expenses into different types, such as mortgage/rent, utilities, personal entertainment, etc. Assign each category a portion of the pie based on the percentage of the overall expense it represents. This will visually show the proportion of each type of expense.

The benefits of this type of analysis are that it provides a clear visual representation of how expenses are distributed across different categories. It helps in identifying the major contributors to expenses, highlighting areas where adjustments can be made, and making informed decisions about budgeting.

The drawback of this analysis is that it simplifies the data into broad categories, potentially losing some granularity. It may not capture every individual expense item or allow for detailed analysis within each category.

When deciding whether to use the standard deviation or variance of data as a measure of dispersion, it depends on the context and the specific requirements of the analysis. The standard deviation and variance are both measures of how spread out the data points are from the mean.

The variance calculates the average of the squared differences between each data point and the mean, whereas the standard deviation is the square root of the variance. In some cases, using the standard deviation may be more appropriate since it is in the same unit as the original data, making it easier to interpret and compare.

Additionally, the standard deviation can be more robust to outliers compared to variance because it takes the square root of the squared differences, reducing the impact of extreme values.

However, the choice between standard deviation and variance depends on the specific circumstances and the analysis goals. Both measures have their own merits, and there is no definitive answer as to which is a better measure of dispersion. It ultimately comes down to the context and preference of the analyst or researcher.