If the average number of textbooks is 16, the standard deviation is 5, and the average age of a professors is 43, with a standard deviation of 8, which data set is more variable?
Textbooks. I will happily critique your reasons why.
FOr your thinking, add one more example: number cows in a pasture, mean 3, standard deviation 3
To determine which data set is more variable, we need to compare the standard deviations of both data sets.
For the textbooks data set, the standard deviation is given as 5. This means the individual values in the data set deviate from the mean, on average, by approximately 5 units.
Similarly, for the professors' age data set, the standard deviation is given as 8. This means the individual values in this data set deviate from the mean, on average, by approximately 8 units.
Comparing the values, we can see that the standard deviation of the professors' age data set (8) is greater than the standard deviation of the textbooks data set (5).
Therefore, the professors' age data set is more variable as it has a larger spread of values from the mean compared to the textbooks data set.