Profitability is very important in business. It is the main reason why companies or businesses are established. Profits ensure that businesses survive and are attractive to investors. Profits are re-invested and are used to expand the business (Sahay, 2018). Also, profits remain the only source of capital if a company or a corporation does not have an investor or any other source of capital. Business profits go hand in hand with the number of customers a company might be having. The higher the number of customers, the higher profits are realized.
Analysis of 2015 profits
The mean value of is calculated using the formula;
This means that taking the total amount of profits for all the companies in the year 2015 and then dividing by n, which is 200. The mean was calculated using the above formula and was found out to be 5609.14. The mean shows the average amount of profit made by the businesses in 2015.
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The median is 5802. It was computed using the formula (n+1)/2. The median indicates the center of all the profits made in 2015. It means that half of the profits lie above 5802 and the other half lies below 5802.
The first quartile of the year 2015 profits is 3606.00. It was obtained using the formula;
0.25(n+1) term. The lower quartile indicates that a quarter of the profits lies below 3606.
Similarly, the third quartile was obtained using the formula 0.75(n+1) and was found out to be 7592.50. This shows that three-quarter of the 2015 profits is below 7592.50.
The minimum value of the 2015 profits is 300. This shows that the lowest amount of profits made by the businesses in that year was $300. In this case, Taylor supply made the least profits in the year 2015.
The maximum value of the 2015 profits is 9973. It shows that the highest amount of profits made by the companies in 2015 was $9973. Mark Maggiacoma business was the most profitable compared to the other companies during that year.
Range = Maximum – Minimum
Using the above formula, a range of $9673 was obtained. It means that the profit margin between the businesses that had the highest amount of profit and the lowest amount of profit was $9673. The difference between the profits made by Mark Maggiacoma Company and Taylor Supply Company was $9673.
A standard deviation of 2524.385 for the 2015 profits was obtained using the formula;
The standard deviation, in this case, measures how the 2015 profits are concentrated around the mean. 2524.385 is relatively a large value; it indicates that the profits are not concentrated around the mean.
The coefficient of variation of 45.04% was obtained using the formula;
Coefficient of variation = (Standard deviation/ Mean) * 100
It points out that the standard deviation is 45.04 % of the mean.
Analysis of 2016 profits
The mean value of 2016 profits is calculated using the formula;
The mean was calculated using the above formula and was found out to be $5177.85. The mean shows the average amount of profit made by the businesses in 2016.
The median is $5101. It was computed using the formula (n+1)/2. The median indicates the center of all the profits made in 2016. It means that half of the profits lie above $5101.0 and the other half lies below $5101.
The first quartile of the year 2016 profits is $2740.50. It was obtained using the formula;
0.25(n+1) term. The lower quartile indicates that 25% of the profits lie below 2740.50.
Similarly, the third quartile was obtained using the formula 0.75(n+1) and was found out to be $7384.50. This shows that 75% of the 2016 profits is below 7384.50.
The minimum value of the 2016 profits is $500. This shows that the lowest amount of profits made by the businesses in that year was $500. In this case, Metro Sandwiches & Salads made the least profits in the year 2016. The maximum value of the 2016 profits is $9957. It shows that the highest amount of profits made by the companies in 2016 was $9957. Paul’s Motor Sales and Services business was the most profitable compared to the other companies during that year.
Range = Maximum – Minimum
Using the above formula, a range of $9457 was obtained. It means that the profit margin between the businesses that had the highest amount of profit and the lowest amount of profit was $9457. The difference between the profits made by Paul’s Motor Sales and Services Company and Metro Sandwiches & Salads Company was $9457.
A standard deviation of $2682.574 for the 2016 profits was obtained using the formula;
The standard deviation, in this case, measures how the 2016 profits are concentrated around the mean. $2682.574. This value is large; it indicates that the profits are not so close to the mean.
The coefficient of variation of 51.81% was obtained using the formula;
Coefficient of variation = (Standard deviation/ Mean) * 100
It indicates that the standard deviation is 51.81% of the mean.
Analysis of the two-year average changes in the daily number of visits
The mean of the daily number of visits is 49.72. It was obtained by averaging the changes in the daily number of visits for all 200 businesses. It means that an average of 49.72 customers visited the companies daily.
The median was calculated and found out to be 51.00. It shows that half of the daily customer number of visits is above 51.00 and the other half is below 51.00
The first quartile is 19.00. It means that 25% of the average changes in the number of daily visits is below 19.00. The third quartile is 82.00. This indicates that 75% of the average changes in the number of daily visits lies below 82.00.
The minimum value of the average number of daily customer visits is -10. It means that the lowest average number of daily customer visits was registered to be -10. Sears Grand registered the lowest average number of daily customer visits. The maximum value is 101. It means that the highest average number of daily customer visits registered was 101. Mark Maggiacoma Company registered the highest average number of customer daily visits.
The range is 111. It is the difference between the highest average number of customer daily visits and the lowest value in that category.
The standard deviation of 33.177 was obtained. This value relatively small, it means the values are so close to mean.
The coefficient of variation is 66.72%. It was obtained by expressing the ratio of standard deviation and mean as a percentage. It means that the standard deviation is 66.72% of the mean.
Analysis of the two-year average number of employees
The mean of the average number of employees is 59.91. It was obtained by using the formula;
It means that the average number of employees per business was 59.91.
The median was calculated and found out to be 62. It shows that half of the average number of employees was above 62 and the other half was below 62.
From the data, the first quartile is 40. It means 25% of the average number of employees lies below 40. On the other hand, the third quartile is 78.75. This indicates that 75% of the average number of employees is below 78.75.
The minimum average number of employees is 20. It means that the company which had the lowest average number of employees had an average of 20 employees. In this case, CC Industrial Sales had the lowest average number of employees. Similarly, the maximum average number of employees is 100. ECS Anchor Supply had the highest average number of employees.
Here, the range is 80. It was obtained by subtracting the minimum average number of employees from the maximum average number of employees.
The standard deviation of 22.625 was obtained by using the formula;
The value is small; it shows the values in the number of employee’s data set are concentrated around the mean.
Using the formula CV = (SD/X̅) * 100, 37.76% coefficient of was obtained. Here, the standard deviation is 37.76% of the mean.
Using Z-score of the percentage changes to identify outliers
To calculate the outliers, the 1 st Quartile, 3 rd Quartile, Interquartile range, Upper bound and Lower bound was calculated using the formulas below;
1 st Quartile = 0.25(n+1) = 50 th position, by arranging the Z-score data in ascending order, the Q1 was -0.46
3 rd Quartile = 0.75(n+1) = 151 st position, by arranging the Z-score data in ascending order, Q3 was 0.073
Interquartile range = 3 rd Quartile - 1 st Quartile
0.073-(-0.46) = 0.53
Upper bound = 3 rd Quartile + (1.5* Interquartile range)
0.073 + (1.5* 0.53) = 0.873
Lower bound = 1 st Quartile – (1.5* Interquartile range)
-0.46-(1.5*0.53) = -1.263
Any value that is not within the Upper bound and Lower bound is termed as an outlier. The calculations were done on the attached excel file using the above formulas. The outliers were Electropower Utility Sales, First Supply Group; Inc, WSA Sales Co. Inc, Sears Grand, Shamrock Computer, RTG Industrial Supply; Inc, American Supply Group, Mr. Spindle, Taylor Supply, Bales Hay Sales, Zero Systems, Howard Sales Co.; Inc, The Jones Shop, and Florida Villa Vacations Inc.
Computing the correlation coefficient
|
Correlations |
||||
Percentage change in profit |
Two Year Avg. change in daily no. of visits |
Two Year Average Number of Employees |
||
| Percentage change in profit | Pearson Correlation |
1 |
-.351 ** |
.078 |
| Sig. (2-tailed) |
.000 |
.272 |
||
| N |
200 |
200 |
200 |
|
| Two Year Avg. change in daily no. of visits | Pearson Correlation |
-.351 ** |
1 |
.028 |
| Sig. (2-tailed) |
.000 |
.696 |
||
| N |
200 |
200 |
200 |
|
| Two Year Average Number of Employees | Pearson Correlation |
.078 |
.028 |
1 |
| Sig. (2-tailed) |
.272 |
.696 |
||
| N |
200 |
200 |
200 |
|
| **. Correlation is significant at the 0.01 level (2-tailed). | ||||
From the above table, the correlation coefficient between the percentage change in profit and the two-year average change in a daily number of visits is -0.351, this shows there exists a negative relationship between the two variables. The scatter plot shows the relationship between the two variables
The correlation coefficient between the percentage change in profit and the two-year number of employees is 0.078. It means that the relationship between the two variables very weak. It is concluded the relationship between the two variables is not significant. This is illustrated in the scatter plot below
Also, the correlation coefficient between the two-year average number of employees and the two average number of daily visits is 0.028. It is clear that the relationship between the two variables is not significant as shown in the scatter plot below
In conclusion, statistics is important in the general growth of a business. Statistical analysis tools such as mean, median, range, standard deviation, and correlation coefficient are used to analyze different types of data in a business. Statistics helps in explaining the direction of growth of the company in terms of profitability, employee, and customer satisfaction (Anderson, 2018). Statistics also helps the management to choose the best decision out of different alternatives. For instance, in the case of a least-performing product, the company might choose to increase investment in the product or shift to a new product.
References
Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D., & Cochrane, J.J. (2018). Essentials of statistics for business and economics (8th ed.). Boston, MA: Cengage Learning.
Sahay, A. (2018). Business analytics . Business Expert Press.
