Question

the dot plot shows the number of hours, rounded to the nearest half hour, it took alexis to box braid the hair of 30 customers. alexis says that the mean time is greater than 7 hours. is she correct? use the drop - down menus to explain. box braids time (h) click the arrows to choose an answer from each menu. the data in the dot plot are skewed to the right and have a median of choose_ hours. based on the shape of the data, the mean time will be choose_ th 6.25 6.5 7 6.75 alexis is choose_

Explanation:

Step1: Find the median

Since there are $n = 30$ data - points, the median is the average of the 15th and 16th ordered data - points. Counting the dots from the left, we find that the 15th and 16th ordered data - points fall on 6.5. So the median is 6.5 hours.

Step2: Analyze the relationship between mean and median for skewed data

For data that is skewed to the right, the mean is greater than the median. Since the median is 6.5 hours and the data is skewed to the right, the mean is greater than 6.5 hours.

Step3: Determine if Alexis is correct

Since the mean is greater than 6.5 hours and we want to know if it's greater than 7 hours. We can estimate the mean using the formula $\bar{x}=\frac{\sum_{i = 1}^{k}x_{i}f_{i}}{n}$, where $x_{i}$ are the data - values and $f_{i}$ are their frequencies. But just from the shape, we know that the long tail on the right will pull the mean up. However, by looking at the distribution, we can see that the mean is not greater than 7 hours.

Answer:

The data in the dot - plot are skewed to the right and have a median of 6.5 hours. Based on the shape of the data, the mean time will be greater than the median. Alexis is incorrect.