Study the results of my research and write the discussion part of it: Results
The simplified express method for calculating the gross margin of an online store was applied to assess the probability of achieving a gross margin within a specified target range of 25-30%. This method was based on key metrics such as the average order value (AOV) and the cost of goods sold (COGS). The method was checked using statistical analysis using z-scores and a normal distribution.
To illustrate the method, the sale of a 4-meter tulle curtain priced at 1,180 UAH, with a COGS of 780 UAH, was used as a benchmark. The gross margin under normal conditions was calculated as follows:

Gross margin=  (1180-780)/1180×100=33.9%      (1)
However, during promotional periods, where discounts ranging from 5% to 30% were applied to 30 best-selling items, the selling price and gross margin fluctuated. For example, with a 20% discount, the price of the tulle curtain decreased to 944 UAH, resulting in a lower gross margin:
Discounted price = 1180 – (1180×0.20) = 944 UAH  (2)
Gross margin=  (944-780)/944×100=17.36%    (3)
To determine the probability of achieving a gross margin within the 25-30% range, a z-score analysis was performed using a mean gross margin of 27% and a standard deviation of 5%. The formula for calculating the probability (P).
P(25%≤Gross margin≤30%)=P((25%-μ)/σ≤Z≤(30%-μ)/σ)    (4)
Where: μ is the mean gross margin; σ is the standard deviation; Z is the standard normal distribution value.
For a 25% gross margin, the z-score was calculated as:
Z_(25 )=  (25-27)/5= -0.4    (5)
For a 30% gross margin, the z-score was calculated as:
Z_(30 )=  (30-27)/5= 0.6  (6)
Using a z-table or statistical software, the probability corresponding to a z-score of -0.4 is approximately 0.3446, while the probability for a z-score of 0.6 is approximately 0.7257. The probability of the gross margin falling between 25% and 30% is the difference between these two values:
P(25%≤Gross Margin≤30%)=0.7257-0.3446=0.3811   (7)
This result indicated that there was approximately a 38.11% chance that the gross margin would be within the desired range of 25-30%. This probability reflects the business’s capacity to maintain a competitive yet profitable pricing strategy, even while implementing discounts ranging from 5% to 30% on a limited number of best-selling items. Since the discounts applied only to 30 products out of the total 2,500-item catalogue, the overall impact of these promotional discounts on the gross margin is mitigated, allowing the business to achieve a stable margin performance within the target range.
To calculate the likelihood that the gross margin rate will be higher than 30% or lower than 25%, it was continued using the z-scores and normal distribution approach. For a gross margin rate higher than 30%, the already calculated the z-score for 30% was used (see formular 7). The probability for Z = 0.6 is approximately 0.7257. This means that the probability of having a gross margin of 30% or lower is 72.57%. Therefore, the probability of having a gross margin higher than 30% is the complement of that value:
P(Gross Margin>30%)=1-0.7257=0.2743  (8)
Thus, there is a 27.43% chance that the gross margin will be higher than 30%.
Conversely, for a gross margin rate lower than 25%, it was calculated the z-score for 25% (see formular 6). The probability for Z = - 0.4 is approximately 0.3446. This is the probability that the gross margin will be lower than 25%:
P(Gross Margin<25%)=0.3446  (9)
Thus, there is a 34.46% chance that the gross margin will be lower than 25%.
Comparison of Manually Calculated Gross Margin and Express Method
In the comparison between the manually calculated gross margins and the express method, it’s crucial to recognise that the data used for the express method calculations was averaged across the entire period, while the manual calculations were split by month. This key distinction in data aggregation influences the results and requires an adjustment to ensure that the comparison is conducted using a similar approach.
Table 1. Data Drawn for the Manual (Traditional) Calculation of AOV and Gross Margin Distributed by Months
	Jan	Feb	Mar	Apr	May	June	July	Aug	Averaged
AOV, UAH	2418	1094	1279	1230	941 	1278 	1323 	1496	1382
Margin, %	34.08	20.34	18.71	26.39	24.64	25.33	27.49	29.88	25.85

With the data from both the manual and express methods now averaged across the same period, we can make a more direct comparison:
(1) AOV Comparison: The average AOV calculated manually is 1382 UAH, which is higher than the 1,200 UAH used in the express method. This discrepancy suggests that the express method underestimates the AOV. The manually calculated AOV may reflect higher-value purchases in some months, particularly in January, which had an exceptionally high AOV (2,418 UAH). The express method, by averaging over the period, smooths out these fluctuations and assumes a more conservative AOV.
(2) Gross Margin Comparison: The average gross margin calculated manually is 25.85%, compared to the express method’s estimate of 27%. The difference here is relatively small (approximately 1.15%), suggesting that the express method provides a reasonably accurate approximation of the overall gross margin. However, the manually calculated margin, which reflects actual month-by-month data, shows a slight underperformance in terms of profitability compared to the express method.
The comparison reveals that the express method, which assumes an AOV of 1,200 UAH and a gross margin of 27%, provides a slightly optimistic estimation when compared to the manually calculated data. The manual calculations, averaging an AOV of 1382 UAH and a gross margin of 25.85%, suggest that the shop had higher average transaction values but a slightly lower margin than estimated by the express method. This could be due to the variability in monthly performance, particularly during months with lower margins (e.g., February and March).
Additionally, the express method does not fully account for months of significant fluctuation, such as January (which had a high margin of 34%) and March (which had a low margin of 18.71%). By averaging across the entire period, the express method smooths out these extremes, making it less sensitive to month-to-month variability.
These findings suggest that the researcher-developed simplified express method provides a reliable and efficient way to calculate the probability of achieving target gross margin ranges. By focusing on key metrics such as AOV and COGS, combined with z-score analysis, this method offers useful insights for managing profitability in an online store, particularly one with a wide range of product prices and promotional strategies.
Limitations and Recommendations
The express method is useful for generating quick, high-level estimates of gross margin but does not capture the detailed month-by-month fluctuations that can significantly affect profitability. As the manually calculated data shows, significant variation in AOV and margin occurs across months, driven by factors such as promotional events, product mix, and consumer behaviour.
To improve the accuracy of the express method, we recommend integrating some form of seasonality adjustment or allowing for month-to-month variation in AOV and discounts. This would provide a more nuanced analysis, especially for businesses with high variability in sales performance.