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?
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?
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To avoid calculation errors in weighted average problems, systematically list the items, their values, and their weights (frequencies). Calculate the product for each row first, then sum those products to get the total value before dividing by the sum of the weights.
Updated On: Oct 3, 2025
- $255
- $268
- $274
- $285
- $300
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
The mean price, or average price, is calculated by dividing the total revenue generated from selling all the cell phones by the total number of cell phones sold. This is also known as a weighted average, where the number of phones sold at each price point serves as the weight.
Step 2: Key Formula or Approach:
The formula for the mean price is:
Mean Price = Total Revenue / Total Number of Phones Sold
where Total Revenue is the sum of (Price of each brand × Number of units sold of that brand).
Step 3: Detailed Explanation:
First, we extract the required data from the given bar chart and dot plot.
Brand P: Number sold = 75, Price per phone = $300
Brand Q: Number sold = 75, Price per phone = $400
Brand R: Number sold = 125, Price per phone = $150
Brand S: Number sold = 150, Price per phone = $350
Brand T: Number sold = 100, Price per phone = $200
Next, we calculate the total revenue generated from all sales.
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 find 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
Rounding to the nearest dollar, we get $274.
Step 4: Final Answer:
The mean price of the cell phones sold by the store is $274.
The mean price, or average price, is calculated by dividing the total revenue generated from selling all the cell phones by the total number of cell phones sold. This is also known as a weighted average, where the number of phones sold at each price point serves as the weight.
Step 2: Key Formula or Approach:
The formula for the mean price is:
Mean Price = Total Revenue / Total Number of Phones Sold
where Total Revenue is the sum of (Price of each brand × Number of units sold of that brand).
Step 3: Detailed Explanation:
First, we extract the required data from the given bar chart and dot plot.
Brand P: Number sold = 75, Price per phone = $300
Brand Q: Number sold = 75, Price per phone = $400
Brand R: Number sold = 125, Price per phone = $150
Brand S: Number sold = 150, Price per phone = $350
Brand T: Number sold = 100, Price per phone = $200
Next, we calculate the total revenue generated from all sales.
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 find 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
Rounding to the nearest dollar, we get $274.
Step 4: Final Answer:
The mean price of the cell phones sold by the store is $274.
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