Textbooks in Professors’ Offices If the average
number of textbooks in professors’ offices is 16, the
standard deviation is 5, and the average age of the
professors is 43, with a standard deviation of 8, which
data set is more variable?
Well, let's see, the first data set represents the number of textbooks in professors' offices, while the second data set represents the age of the professors. Comparing the two, it seems like the age of the professors has a higher standard deviation. So, I guess you could say that the professors are more variable in terms of their age, not necessarily their textbooks! Age tends to creep up on people and make things more unpredictable.
To determine which data set is more variable, we can compare the standard deviations of the two data sets.
In this case, we have two data sets:
- Data set 1: Number of textbooks in professors' offices
- Data set 2: Age of professors
Given that the standard deviation for data set 1 (number of textbooks) is 5, and the standard deviation for data set 2 (age of professors) is 8, we can compare these values.
Since the standard deviation for data set 2 (age of professors) is larger (8) compared to data set 1 (number of textbooks) which is 5, we can conclude that the data set of the age of professors is more variable.
To determine which data set is more variable, we need to compare the standard deviations of both data sets.
Data Set 1:
Average number of textbooks = 16
Standard deviation of textbooks = 5
Data Set 2:
Average age of professors = 43
Standard deviation of age = 8
To compare the variability, we look at the standard deviation. The greater the standard deviation, the more spread out the data is from the mean, indicating higher variability.
In this case, the standard deviation of textbooks is 5, while the standard deviation of professors' age is 8. Therefore, the data set related to professors' age is more variable since its standard deviation is greater.
Keep in mind that standard deviation alone does not provide a complete picture of the differences in variability between the two data sets. It is always good to consider other measures of variability as well.