Final answer:
Manuel's data is more spread out because of higher variance, while Gretchen's data is more spread out because of higher interquartile range (IQR).
Step-by-step explanation:
The spread of data refers to how widely the data values are distributed from the mean. In this case, we are comparing the spread of Manuel's data and Gretchen's data.
To determine which data set is more spread out, we can consider different measures of spread, such as variance, standard deviation, range, and interquartile range.
In option A, it states that Manuel's data is more spread out because of a higher variance. Variance measures how far each data point is from the mean, so a higher variance indicates greater spread. This is a valid explanation for Manuel's data being more spread out.
Option B suggests that Gretchen's data is more spread out because of lower standard deviation. However, the standard deviation actually measures how far data values are from their mean, so a higher standard deviation would indicate greater spread.
Option C states that Manuel's data is more spread out because of a lower range. The range is simply the difference between the maximum and minimum values in a data set, so a lower range does not necessarily imply greater spread. This explanation is incorrect.
Option D suggests that Gretchen's data is more spread out because of a higher interquartile range (IQR). The IQR measures the spread of the middle 50% of the data, so a higher IQR would indicate greater spread. This is a valid explanation for Gretchen's data being more spread out.
In conclusion, based on the given options, Manuel's data is more spread out because of a higher variance, as stated in option A.