Flight Time The following data represent the flight time (in minutes) of a random sample of seven flights from Las Vegas, Nevada, to Newark, New Jersey, on United Airlines. Compute the mean, median, and mode flight time.


282, 270, 260, 266, 257, 260, 267

Verified step by step guidance

1. Step 1: Organize the data in ascending order to make it easier to find the median and mode. The data points are: 282, 270, 260, 266, 257, 260, 267. Sort them from smallest to largest.
2. Step 2: Calculate the mean (average) flight time by summing all the flight times and then dividing by the number of flights. Use the formula: \(\text{Mean} = \frac{\sum x_i}{n}\), where \(x_i\) are the flight times and \(n\) is the number of flights.
3. Step 3: Find the median flight time, which is the middle value in the ordered data set. Since there are 7 data points (an odd number), the median is the value at position \(\frac{n+1}{2}\). Identify this value in the sorted list.
4. Step 4: Determine the mode, which is the flight time that appears most frequently in the data set. Look for any repeated values and identify the one with the highest frequency.
5. Step 5: Summarize your findings by stating the mean, median, and mode flight times based on the calculations and observations from the previous steps.

Key Concepts

Mean

The mean is the average value of a data set, calculated by summing all the observations and dividing by the number of observations. It provides a measure of central tendency that reflects the overall level of the data. For example, adding all flight times and dividing by seven gives the mean flight time.

Median

The median is the middle value in an ordered data set, which divides the data into two equal halves. To find it, arrange the data from smallest to largest and select the middle number. The median is useful for understanding the central tendency when data may be skewed or have outliers.

Mode

The mode is the value that appears most frequently in a data set. It helps identify the most common observation, which can be important in understanding typical outcomes. In the flight time data, the mode is the flight time that occurs more than once.