The same car at three different dealerships had a median price of $14,833.02. The mean price was
$14,544.43 and the range of prices was $1476.24. What were the three prices?
(low price + median price + high price)/3 = 14544.43 (the mean price).
Therefore, lp + median + hp = 3*14,544.43 = 43,633.29.
Subtract the median and lp + hp = 43,633.29 - 14833.02 = 28,800.27.
That divided by 2 = 14400.135.
So add 1/2 the range to this and subtract 1/2 the range from this to get the lp and the hp.
If I didn't make an error, the lp is 13662.01 and the hp is 15138.25.
Check it out. The range is 1476.24.
mean is 14544.43 (One of the numbers comes out with an 0.005 so it isn't exactly a penny)
To solve this problem, we'll use the information provided and apply some mathematical calculations. Let's first find the middle price, also known as the median.
Step 1: Calculate the total range
The range is the difference between the highest and lowest prices. In this case, the range is given as $1476.24.
Range = $1476.24
Step 2: Calculate the middle price (median)
Since we have three prices, the median is the middle value. Since the median price is given as $14,833.02, it must be the middle price.
Therefore, the median price = $14,833.02
Step 3: Calculate the sum of all three prices
To find the average (mean) price, we'll need the sum of all three prices. Let's assume the three prices are A, B, and C.
Total sum = A + B + C
Step 4: Calculate the mean price
The mean price is given as $14,544.43.
Mean = Total sum / Number of prices
$14,544.43 = (A + B + C) / 3
Step 5: Find the individual prices
We can now solve the equation using the information we have.
(A + B + C) / 3 = $14,544.43
Now, let's substitute the median price into the equation:
($14,833.02 + B + C) / 3 = $14,544.43
Multiply both sides by 3 to remove the fraction:
$14,833.02 + B + C = $43,633.29
Step 6: Find B and C
Since the total sum includes all three prices, we can calculate B and C.
B + C = $43,633.29 - $14,833.02
B + C = $28,800.27
Step 7: Use the range to find A
The range is given as $1476.24, which means the difference between the highest and lowest price.
Since the median price is in the middle, the highest and lowest prices must be equally distant from the median.
Therefore, the difference between the highest and lowest price is $1476.24 / 2 = $738.12.
To find A, we can subtract this difference from the median:
A = $14,833.02 - $738.12
A = $14,094.90
Step 8: Calculate the individual prices
Now that we have A, B, and C, we can list the three prices:
A = $14,094.90
B = $28,800.27 - C
C = The remaining price to make the sum equal to $43,633.29
This information is all we need to determine the three prices.
To find the three prices, we need to make use of the information provided. Let's go step by step:
Step 1: Find the middle price (median):
Since we have the median price as $14,833.02, this means that one of the prices lies in the middle among the three.
Step 2: Find the mean price:
The mean price is given as $14,544.43. The mean is the sum of all the prices divided by the number of prices. We can use this information to find the total of the three prices.
Step 3: Find the range of prices:
The range is the difference between the highest and lowest prices. Here, we are given that the range is $1476.24. This range will help us find the difference between the highest and lowest prices.
Let's proceed with the calculations:
Step 1: Finding the middle price (median):
We know that the median price is $14,833.02, so one of the prices must be $14,833.02.
Step 2: Finding the mean price:
We know that the mean price is $14,544.43, and we have three prices. Let's assume the three prices are P1, P2, and P3. We can set up the following equation:
(P1 + P2 + P3) / 3 = $14,544.43
Step 3: Finding the range of prices:
We are given that the range is $1476.24. Since the range is the difference between the highest and lowest prices, we can set up the following equation:
Highest Price - Lowest Price = $1476.24
Now, we have two equations with two unknowns (P1, P2, and P3). We can solve these equations to find the three prices.