Buying a Car The following data represent the asking price, in dollars, for a random sample of 2014 coupes (a two-door car) and a random sample of 2014 Chevy Camaros.
a. Find the mean and standard deviation price for each sample.

Verified step by step guidance

1. Step 1: Organize the data for each sample separately. For the Coupes, list all the asking prices: 25991, 15900, 16900, 24948, 23791, 20990, 19900, 17900, 16888, 15995, 15891, 13991, 12900, 11995, 9900. For the Camaros, list all the asking prices: 24949, 24948, 23061, 22150, 21855, 20990, 19950, 19593, 18995, 17849, 16900, 16440, 15987, 15900, 15891.
2. Step 2: Calculate the mean (average) price for each sample. Use the formula for the mean: \[\text{Mean} = \frac{\sum_{i=1}^n x_i}{n}\] where \(x_i\) are the individual prices and \(n\) is the number of prices in the sample.
3. Step 3: Calculate the standard deviation for each sample to measure the spread of the prices. Use the formula for the sample standard deviation: \[s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2}\] where \(\bar{x}\) is the mean calculated in Step 2, and \(n\) is the number of prices.
4. Step 4: For each sample, subtract the mean from each price to find the deviations, square each deviation, sum all squared deviations, then divide by \(n-1\) (degrees of freedom), and finally take the square root to get the standard deviation.
5. Step 5: Summarize your results by reporting the mean and standard deviation for both the Coupes and the Camaros samples, which will give you an understanding of the central tendency and variability of the asking prices in each group.

Key Concepts

Mean (Average)

The mean is the sum of all data values divided by the number of values. It represents the central tendency or typical value of a dataset. Calculating the mean price for each sample helps summarize the average asking price of coupes and Camaros.

Standard Deviation

Standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation means prices are close to the mean, while a high one indicates more spread. It helps understand the consistency of car prices within each sample.

Comparative Statistical Analysis

Comparing the mean and standard deviation of two samples allows us to analyze differences in price levels and variability between coupes and Camaros. This comparison is essential for making informed decisions or conclusions about the two groups.