Question

The students in Ms. Rodriguez's class reported the number of hours they spend exercising in a
typical week. They recorded their answers in a dot plot.
Ms. Rodriguez's Class
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Hours Spent Exercising Based on the spread of the data, would the mean or median be a better measure of center?

Answer 1

To determine whether the mean or median would be a better measure of center for the data reported by Ms. Rodriguez's class regarding hours spent exercising, we need to consider the distribution and spread of the data.

1. **Mean**: The mean is calculated by adding all the values together and dividing by the number of values. The mean can be affected by extreme values (outliers) in the data.

2. **Median**: The median is the middle value when the data is arranged in order. It is less affected by outliers and skewed data.

If the dot plot indicates that the distribution of hours spent exercising is skewed (for example, if a few students reported a very high number of hours compared to others), the mean could be disproportionately influenced by those higher values. In such cases, the median would provide a better representation of the typical amount of exercise time.

Conversely, if the data is symmetrically distributed without outliers, the mean might be a better measure of central tendency since it takes into account all values.

Without a visual representation of the dot plot, you would typically consider the following:

- If the data has a significant number of outliers or is skewed, the **median** would be a better measure.
- If the data is fairly symmetric and there are no extreme values, the **mean** could be appropriate.

In summary, based on the spread of the data and potential skewness or presence of outliers, if those conditions apply, the median would generally be a better measure of center.