Using and Interpreting Concepts


Finding and Discussing the Mean, Median, and Mode In Exercises 17–34, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why.


Prices (in dollars) of Flights from Chicago to Alanta

Verified step by step guidance

1. Step 1: Extract the data points from the graph. Each dot represents a flight price. Count the number of dots at each price level to determine the frequency of each price. For example, if there are 4 dots at \$180, the frequency of \$180 is 4.
2. Step 2: Calculate the mean (average) price. To do this, multiply each price by its frequency, sum these products, and then divide by the total number of data points. The formula is: $\mathrm{Mean}=\frac{\sum xf}{n}$, where x is the price, f is the frequency, and n is the total number of data points.
3. Step 3: Find the median price. Arrange all the data points in ascending order (if not already arranged). The median is the middle value if the total number of data points is odd, or the average of the two middle values if the total number of data points is even.
4. Step 4: Determine the mode of the data. The mode is the price that appears most frequently in the dataset. Identify the price with the highest frequency.
5. Step 5: Interpret the results. Discuss whether the mean, median, and mode are good measures of the center for this dataset. Consider factors such as the distribution of the data (e.g., skewness) and whether any outliers might affect the mean.

Key Concepts

Mean

The mean, or average, is calculated by summing all the values in a dataset and dividing by the number of values. It provides a central value that represents the overall dataset but can be influenced by extreme values (outliers). In the context of flight prices, the mean gives an idea of the typical cost of a flight, but may not reflect the most common price if there are significant outliers.

Median

The median is the middle value of a dataset when it is ordered from least to greatest. If there is an even number of observations, the median is the average of the two middle values. This measure is particularly useful for skewed distributions, as it is less affected by outliers than the mean. In the flight prices example, the median will indicate the price at which half of the flights are cheaper and half are more expensive.

Mode

The mode is the value that appears most frequently in a dataset. It is a useful measure for understanding the most common price in a set of flight prices. In cases where there are multiple modes (bimodal or multimodal distributions), it can indicate a range of popular prices. In the given data, identifying the mode helps to understand which flight price is most prevalent among the options available.