Exam Time The following data represent the amount of time (in minutes) a random sample of eight students took to complete the online portion of an exam in Sullivan’s Statistics course. Compute the mean, median, and mode time.


60.5, 128.0, 84.6, 122.3, 78.9, 94.7, 85.9, 89.9

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: 60.5, 128.0, 84.6, 122.3, 78.9, 94.7, 85.9, 89.9. Sort these values from smallest to largest.
2. Step 2: Calculate the mean (average) by summing all the data points and then dividing by the number of data points. Use the formula: \(\text{Mean} = \frac{\sum x_i}{n}\), where \(x_i\) are the data points and \(n\) is the number of data points.
3. Step 3: Find the median, which is the middle value when the data is ordered. Since there are 8 data points (an even number), the median is the average of the 4th and 5th values in the sorted list. Use the formula: \(\text{Median} = \frac{x_{(n/2)} + x_{(n/2 + 1)}}{2}\).
4. Step 4: Identify the mode, which is the value that appears most frequently in the data set. Check if any value repeats; if no value repeats, then the data set has no mode.
5. Step 5: Summarize your findings by reporting the mean, median, and mode 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 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 exam times and dividing by eight gives the mean time.

Median

The median is the middle value in an ordered data set, separating the higher half from the lower half. To find it, arrange the data in ascending order and identify the middle number; if there is an even number of observations, the median is the average of the two middle values. It is useful for understanding the central tendency when data are skewed.

Mode

The mode is the value that appears most frequently in a data set. It helps identify the most common observation, which can be useful in understanding patterns or preferences. A data set may have one mode, multiple modes, or no mode if all values are unique.