8. Which data is more spread: Data Set A or Data Set B? Explain your choice.
Data Set A has a mean of 70, a max of 85, a min of 58, a standard deviation of 12.3, and a mode of 84
Data Set B has a mean of 72, a max of 88, a min of 72, a standard deviation of 10.8, and a mode of 86.
To determine which data set is more spread, we need to compare the measures of spread for each data set. In this case, we have the standard deviation for both Data Set A (12.3) and Data Set B (10.8), which is a commonly used measure of spread.
The standard deviation measures the average amount of variability or dispersion of the data points from the mean. A larger standard deviation indicates a greater spread of the data points.
Comparing the standard deviations:
- Data Set A has a standard deviation of 12.3,
- Data Set B has a standard deviation of 10.8.
Since the standard deviation of Data Set A (12.3) is greater than that of Data Set B (10.8), it means that the data points in Data Set A are more spread out or have a greater variability compared to Data Set B.
Therefore, based on the standard deviation values, Data Set A is more spread than Data Set B.