leasures of The dot plot of time (in minutes) it takes employees to drive to work is shown below. Find the mean, median, and mode of the data. If any measure cannot be found or does not represent the center of the data, explain why.

To determine the **mean**, **median**, and **mode** from a dot plot of employees' driving times to work, you can follow these steps. Since I don't have the specific data from your dot plot, I'll provide a general guide on how to calculate each measure. If you provide the data points or a detailed description of the dot plot, I can offer more precise calculations. ### **1. Mean (Average)** The mean is the sum of all data points divided by the number of data points. **Steps to Calculate the Mean:** 1. **List all the data points**: Extract each driving time from the dot plot. 2. **Sum the data points**: Add all the driving times together. 3. **Count the number of data points**: Determine how many employees' driving times are represented. 4. **Divide the total sum by the number of data points**: This gives the mean driving time. **Formula:** \[ \text{Mean} = \frac{\sum \text{Driving Times}}{\text{Number of Employees}} \] **Example:** If the driving times (in minutes) are: 10, 20, 20, 30, 40 \[ \text{Mean} = \frac{10 + 20 + 20 + 30 + 40}{5} = \frac{120}{5} = 24 \text{ minutes} \] ### **2. Median (Middle Value)** The median is the middle value when the data points are ordered from least to greatest. If there's an even number of data points, the median is the average of the two middle numbers. **Steps to Calculate the Median:** 1. **Order the data points**: Arrange the driving times in ascending order. 2. **Find the middle position**: - If odd number of data points: The median is the middle number. - If even number of data points: The median is the average of the two middle numbers. **Example:** For an odd number of data points: 10, 20, 20, 30, 40 \[ \text{Median} = 20 \text{ minutes} \quad (\text{the third value}) \] For an even number of data points: 10, 20, 20, 30 \[ \text{Median} = \frac{20 + 20}{2} = 20 \text{ minutes} \] ### **3. Mode (Most Frequent Value)** The mode is the data point that appears most frequently in the dataset. **Steps to Identify the Mode:** 1. **Tally the frequencies**: Count how many times each driving time appears. 2. **Identify the highest frequency**: The driving time(s) with the highest count is the mode. **Example:** For driving times: 10, 20, 20, 30, 40 \[ \text{Mode} = 20 \text{ minutes} \quad (\text{appears twice}) \] If no number repeats, the dataset has **no mode**. If multiple numbers share the highest frequency, the dataset is **bimodal** or **multimodal**. ### **When a Measure May Not Represent the Center Appropriately** - **Mean**: Can be skewed by extremely high or low values (outliers), making it less representative of the central tendency in such cases. - **Median**: Generally a good measure of center, especially with skewed data, but may not account for the distribution's nuances. - **Mode**: Useful for identifying the most common value but doesn't consider all data points, so it might not fully represent the data's center, especially in uniformly distributed datasets. ### **Conclusion** If you provide the specific data points or a detailed description of the dot plot, I can help you calculate the exact mean, median, and mode for your dataset. Additionally, understanding the distribution of your data (e.g., skewed, symmetric, bimodal) can help determine which measure best represents the center of your dataset.