Introduction to Statistics MATH 1300
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Introduction to Statistics MATH 1300
• This document serves as an example of how to discuss your outputs for your final
project. Do not limit yourself to only what I have discussed in this document. You
should give rich in-depth interpretations in your report. This is a guide on some of the main things you should include in your analysis and how to present your report.
• Do not plagiarize what I wrote because the data set is not the same as in the final project. You should conduct your own analysis and write in your own words.
• Include an introduction and a conclusion summarizing your results.
• Your report must be written in essay format with your graphs and charts in the appendix as in this example.
• Submit both the word document and Excel file
Interpretations
Interpreting a Qualitative Variable
Customers used a variety of web browsers to visit the popular Apparel website. The browsers used by customers are Internet Explorer, Firefox, Chrome and other type of web browsers. 47% of customers used Internet Explorer, 30% used Firefox and 12% used both Chrome and other browsers to visit the website. Notably, of the 60 customers, 46 of them use either Firefox or Internet Explorer (see table 1 and chart 1 in Appendix A).
**Note the same data set was not used in the discussion below. This is just a guide on how to interpret your results**
Interpreting Descriptive Statistics
There were 50 customers who visited the Apparel website. While on the website, customers spend a minimum of $17.84 and a maximum of $158.51. Majority of the customers spend between $57.84 and $77.84 which accounts for 28% of customers sales followed by 26% of customers who spend between $37.84 and $57.84 (see table 2aAppendix A). The typical amount spent by customers falls between $3.44 and $132.82 which accounts for 75% of customer spending. This means that about 38 of customer spend within this typical spending range.
The distribution of the amount customers spend is right-skewed. From table 2a and graph 2a in Appendix A, one can observe that the amount most customers spend falls towards the left of the distribution. Also, based on the box-and-whisker plot, most customers spend the median amount of $62.15 and below (see plot 1 in Appendix A).
On average, customers spend $68.13 with a median amount of $62.15. The average difference in the amount spent is $32.34. This large standard deviation indicates that the amounts spent by customers are more spread about the mean. That is, the amount customers spend are not close together. This is further highlighted by the wide range of $140.67 in the amount spent.
About a quarter (25%) of the customers spend $43.85 or less, about half (50%) of them spend $62.15 or less and about three-quarters (75%) of them spend $84.13 or less. It is of importance to note that the interquartile range of $42.29 shows a wide variability in customer spending. Like what was observed from the standard deviation (see Table 2b in Appendix A).
Interpreting Confidence Interval
The confidence interval for the amount spent by customers on the Apparel website is $58.94 < μ < $77.32. This means that with 95% confidence, one can conclude that the population mean amount spent by customers is between $58.94 and $77.32 (see table 2a in Appendix A).
Interpreting Correlation & Regression
Based on the scatter plot, there is a positive linear relationship between the number of pages viewed by customers and the time spent on the website. One can observe that the data values show a linear relationship between the two variables. Looking at the scatter plot from left to right, as the number of pages viewed increase, the time spent on the website tend to increase. The correlation coefficient r = 0.5956 describes a positive linear relationship between pages viewed and time spent (see table 3 in Appendix B). This implies that there is a moderately strong linear relationship between the time spent on the website and the pages viewed by customers.
The linear regression equation for the amount spent and pages viewed is y = 1.7724x + 4.2666 (see scatterplot in Appendix B) where y predicts the time spent when x number of pages were viewed by customers. Based on the regression model, the time spent on the website increases by about 1.77 minutes for every additional page viewed by customers.
**Note the same data set was not used in the discussion below. This is just a guide on how to interpret your results**
Interpreting Side by Side Box Plot
Among the 111 business graduates there are more (21) finance graduates than information systems graduates (16). The starting salary distribution of information systems is right-skewed compared to the starting salary distribution finance graduates which is left-skewed. This means that most information systems graduates have lower starting salaries than finance graduates. When comparing the minimum starting salaries finance graduates ’ starting salaries are higher with a difference of $1,440. On the other hand, the maximum starting salaries of information systems is slightly higher with only a difference of $360. In fact, the maximum starting salary of $64,800 for finance graduates is an outlier.
This implies that this starting salary is unusual for these graduates. On average, information systems graduates have higher starting salaries. About 25% of information system graduates’ starting salaries is $49,530 or less, about 50% have starting salaries of $51,780 or less and about 75% have starting salaries of $65,160 or less compared to finance graduates who have about 25% of their starting salaries that are $40,200 or less, 50% have staring salaries of $49,200 or less and 75% with salaries of $64,800 or less. Overall, finance graduates have lower starting salaries than information systems graduates despite its left-skewed distribution (see table 4 in Appendix C). As previously mentioned, most finance graduates salaries tend to fall on the higher end of the distribution.
There is more variation in the starting salaries of finance graduates than information systems graduates due to its high interquartile range of $11,850. This implies that the starting salaries of information systems graduates is not at as spread out as finance graduates. About 50% of the starting salaries have a difference between $7,395 and $11,850 (refer to the Interquartile range, IQR in table 4 of Appendix C).
2023-08-24