5. Sales. An auto dealer’s sales numbers are shown in the table below. Find for each month the mean, median, and mode prices of the cars she sold. Round your answers to the nearest dollar. Price
May June July
$20,000 22 25 24
$15,000 49 24 24
$12,500 25 49 49
To find the mean, median, and mode prices of the cars sold for each month, follow these steps:
May:
For May, we have the following prices: $20,000, $15,000, and $12,500.
Mean: To find the mean price, add up all the prices and divide by the number of prices. So,
Mean = (20,000 + 15,000 + 12,500) / 3 = 47,500 / 3 ≈ $15,833.33
Median: To find the median price, arrange the prices in ascending order and find the middle value.
The prices in ascending order: $12,500, $15,000, $20,000.
Since there are three prices, the middle value is the second price: $15,000.
Mode: The mode is the price that appears most frequently. In this case, there is no mode as none of the prices repeat.
June:
For June, we have the following prices: $22,000, $49,000, and $25,000.
Mean: Mean = (22,000 + 49,000 + 25,000) / 3 = 96,000 / 3 = $32,000
Median: The prices in ascending order: $22,000, $25,000, $49,000.
Since there are three prices, the middle value is the second price: $25,000.
Mode: The mode is the price that appears most frequently. In this case, there is no mode as none of the prices repeat.
July:
For July, we have the following prices: $24,000, $24,000, and $49,000.
Mean: Mean = (24,000 + 24,000 + 49,000) / 3 = 97,000 / 3 = $32,333.33
Median: The prices in ascending order: $24,000, $24,000, $49,000.
Since there are three prices, the middle value is the average of the two middle prices: ($24,000 + $24,000) / 2 = $24,000.
Mode: The mode is the price that appears most frequently. In this case, the mode is $24,000.
So the mean, median, and mode prices for each month are as follows:
May: Mean ≈ $15,833, Median = $15,000, Mode N/A
June: Mean = $32,000, Median = $25,000, Mode N/A
July: Mean ≈ $32,333, Median = $24,000, Mode = $24,000
May 9000,8000,7000
June 15000,12000,10000
July 12200,12000,11000