A dealership sold 15 cars last month. The purchase price of the cars, rounded to the nearest thousand, is represented in the table

Purchase Price/# of cars sold
$15,000 3
$20,000 4
$23,000 5
$25,000 2
$45,000 1
A.Find the mean and median
B. Which measures best represents the data? Use the results to support your answer.
C. What is the outlier and how does it affect the data?

Mean = (15000x3+20000x4...)/(3+4+5+2+1)

= 22.33333
Median = 23000

Outlier would depend on what how you define it, but it would probably be 45000 and it'd affect the mean and standard deviation of the plot.

To find the mean and median from the given data, you will follow these steps:

Step 1: Multiply each purchase price by the corresponding number of cars sold to find the total value for each row.

Step 2: Add up all the total values obtained to find the sum.

Step 3: Add up the number of cars sold to find the total count.

Step 4: Divide the sum obtained in Step 2 by the total count obtained in Step 3 to find the mean.

Step 5: Arrange the purchase prices in ascending order.

Step 6: Find the middle value. If there is an odd total count, the middle value is the median. If there is an even total count, find the average of the two middle values to get the median.

Let's go through each step to find the mean and median:

A. Finding the mean:
- $15,000 x 3 = $45,000
- $20,000 x 4 = $80,000
- $23,000 x 5 = $115,000
- $25,000 x 2 = $50,000
- $45,000 x 1 = $45,000

Sum = $45,000 + $80,000 + $115,000 + $50,000 + $45,000 = $335,000
Total count = 3 + 4 + 5 + 2 + 1 = 15

Mean = $335,000 / 15 = $22,333.33 (Round to the nearest whole number: $22,333)

B. Finding the median:
Arranging the purchase prices in ascending order: $15,000, $20,000, $23,000, $23,000, $23,000, $23,000, $25,000, $25,000, $45,000
The total count is 15, which is odd.

Therefore, the median is the middle value, which is the 8th value in the list: $23,000

B. Which measure best represents the data?
The mean, $22,333, and the median, $23,000, both provide different insights into the data.

The mean represents the average purchase price per car sold. It gives an indication of the typical purchase price in this dataset. However, the mean can be influenced by outliers, which might distort the overall picture.

The median represents the middle value, which in this case is $23,000. It gives an indication of the purchase price that separates half of the cars sold at a higher price and half at a lower price. The median is generally used when the data has outliers or extreme values, as it is less affected by them.

To determine which measure best represents the data, we need to analyze the impact of outliers.

C. Identifying the outlier and its effects:
Looking at the data, we notice that there is only one purchase price of $45,000, while the other prices range from $15,000 to $25,000. The purchase price of $45,000 is the outlier in this dataset.

The outlier affects the data by significantly pulling up the mean. Without the outlier, the mean would be lower, closer to the median. The outlier creates a skewness in the data and can distort the overall picture when analyzing the average purchase price.

In this scenario, the median, $23,000, is likely a better representation of the purchase prices because it is less influenced by the outlier. It provides a central value that divides the data equally, making it more robust against extreme values.

A. Let's find the mean and median for the purchase price of the cars sold:

Mean calculation:
Total purchase price = (15000 * 3) + (20000 * 4) + (23000 * 5) + (25000 * 2) + (45000 * 1)
= 45000 + 80000 + 115000 + 50000 + 45000
= 340,000

Total number of cars sold = 3 + 4 + 5 + 2 + 1
= 15

Mean = Total purchase price / Total number of cars sold
= 340,000 / 15
= $22,666.67

So, the mean purchase price is $22,666.67.

Median calculation:
To find the median, we need to arrange the purchase prices in ascending order:

$15,000, $15,000, $15,000, $20,000, $20,000, $20,000, $20,000, $23,000, $23,000, $23,000, $23,000, $23,000, $25,000, $25,000, $45,000.

There are a total of 15 numbers, so the median will be the 8th value.

Median = $23,000

B. To determine which measure best represents the data, we need to consider the distribution and any outliers. The mean is influenced by extreme values, so if there are any outliers, it may skew the average. The median, on the other hand, is not affected by outliers as it looks at the middle value.

C. Looking at the data, we can observe that the purchase price of $45,000 appears to be an outlier since all other prices range between $15,000 and $25,000. An outlier is a data point that significantly deviates from the other data points. In this case, the outlier of $45,000 is higher compared to the other prices.

The presence of an outlier affects the data by pulling the mean towards higher values. It increases the average purchase price, making it less representative of the majority of prices. However, the median is not affected by the outlier and represents the middle value, which may be more representative of the typical purchase price.