Question

At a certain store for a certain month, in a chart given below, the price per cell phone (in dollars) is shown by dots (read from right hand side vertical axis) and the number of cell phones sold (read from left hand side vertical axis). 

What is the mean price (nearest to a dollar) of the cell phone sold by the store in that month? 
 

Hint:

When calculating the mean from a frequency chart, always remember it's a weighted average. A common error is to take the simple average of the prices ($150, $200, $300, $350, $400), which would be incorrect. The number of items sold at each price point acts as the 'weight'. Always calculate Total Value / Total Count.

Answer 1

Step 1: Understanding the Concept: 
The mean price of the cell phones is the average price of all phones sold. Since different brands have different prices and were sold in different quantities, we need to calculate a weighted average. The mean price is the total revenue from all phones sold divided by the total number of phones sold. 
Step 2: Key Formula or Approach: 
The formula for the mean price in this context is: 
Mean Price = Total Revenue / Total Number of Phones Sold 
Where: 
Total Revenue = Σ (Number of phones of a brand × Price of that brand) 
Total Number of Phones Sold = Σ (Number of phones of each brand) 
Step 3: Detailed Explanation: 
First, we extract the data for the number of phones sold (bars) and their corresponding prices (dots) for each brand from the chart. 

Brand P: Number sold = 75, Price = $300 

Brand Q: Number sold = 75, Price = $400 

Brand R: Number sold = 125, Price = $150 

Brand S: Number sold = 150, Price = $350 

Brand T: Number sold = 100, Price = $200 

Next, we calculate the total revenue by multiplying the number of units sold by the price for each brand and summing the results. 

Revenue from Brand P = (75 × 300 = $22,500) 

Revenue from Brand Q = (75 × 400 = $30,000) 

Revenue from Brand R = (125 × 150 = $18,750) 

Revenue from Brand S = (150 × 350 = $52,500) 

Revenue from Brand T = (100 × 200 = $20,000) 
Total Revenue = $22,500 + $30,000 + $18,750 + $52,500 + $20,000 = $143,750 
Now, we calculate the total number of cell phones sold. 
Total Number of Phones Sold = 75 + 75 + 125 + 150 + 100 = 525 
Finally, we calculate the mean price. 
Mean Price = $143,750 / 525 ≈ $273.8095... 
The question asks for the mean price to the nearest dollar. We round 273.8095... to the nearest dollar, which is $274. 
Step 4: Final Answer: 
The mean price of the cell phones sold by the store, rounded to the nearest dollar, is $274.