Two food carts' profits comparison

What is the difference in dollars between the lowest profits of Cart A and Cart B?

Given that the medians and the largest profit values are the same for both carts, how can we calculate the difference in dollars between the lowest profits of Cart A and Cart B?

Solution: Calculating the Difference in Profits

To find the difference in dollars between the lowest profits of Cart A and Cart B, we need to use the information provided and set up equations to solve for it. Firstly, let's establish some variables:

Let N be the number of weeks (N = 3 in this case).

Let P_A1, P_A2, P_A3 be the weekly profits for Cart A in weeks 1, 2, and 3.

Let P_B1, P_B2, P_B3 be the weekly profits for Cart B in weeks 1, 2, and 3.

We know that the medians and the largest profit values are the same for both carts. Therefore, we have the following equations:

M = (P_A2 + P_A3) / 2 = (P_B2 + P_B3) / 2

L = max(P_A1, P_A2, P_A3) = max(P_B1, P_B2, P_B3)

Next, consider the means for each cart:

Mean_A = (P_A1 + P_A2 + P_A3) / N

Mean_B = (P_B1 + P_B2 + P_B3) / N

Given that Mean_A = Mean_B + $27, we can set up the following equation:

(P_A1 + P_A2 + P_A3) / N = (P_B1 + P_B2 + P_B3) / N + $27

To find the difference between the lowest profits of Cart A and Cart B, we compare the means:

Difference = Mean_A - Mean_B = ($27 + (P_B1 + P_B2 + P_B3) / N) - (P_B1 + P_B2 + P_B3) / N

Therefore, the difference in dollars between the lowest profits of Cart A and Cart B is $27.

Exploring the Calculation Method

By considering the medians, largest profits, and means of the weekly profits for both carts, we were able to develop a strategy to determine the difference in dollars between the lowest profits of Cart A and Cart B. This problem showcases the importance of understanding how different statistical measures can be used to compare and analyze data.

Through the equations we set up and the logic applied, we were able to identify that the primary factor affecting the difference in profits between the two carts was the discrepancy in the average profits. The $27 variance in the means directly led to the $27 difference in the lowest profits.

By leveraging these mathematical concepts and analytical techniques, we can gain insights into the financial performance of businesses and make informed decisions based on statistical data. Understanding how to interpret and analyze financial data is crucial in various industries and fields of study.