A psychologist interested in political behavior measured the square footage of the desks in the official office of four U.S. governors and of four chief executive officers (CEOs) of major U.S. corporations. The figures for the governors were 44, 36, 52, and 40 square feet. The figures for the CEOs were 32, 60, 48, and 36 square feet. (a) Figure the means and standard deviations for the governors and for the CEOs. (b) Explain, to a person who has never had a course in statistics, what you have done. (c) Note the ways in which the means and standard deviations differ, and speculate on the possible meaning of these differences, presuming that they are representative of U.S. governors and large corporations’ CEOs in general.

What don't you understand about this assignment?

To find the means and standard deviations for the governors and CEOs, we will perform some calculations:

(a)
To find the mean (average):
- Add up all the square footage values for the governors and CEOs separately.
- Divide each total by the number of values.
- The resulting values will be the means.

For the governors:
Mean (Governors) = (44 + 36 + 52 + 40) / 4

For the CEOs:
Mean (CEOs) = (32 + 60 + 48 + 36) / 4

To find the standard deviation:
- Calculate the deviation of each value from the mean (subtract the mean from each value).
- Square each of these deviations.
- Calculate the mean of these squared deviations.
- Take the square root of the mean squared deviations.
- The resulting values will be the standard deviations.

For the governors:
- Calculate the deviation of each value from the mean of governors.
- Square each of these deviations.
- Calculate the mean of these squared deviations.
- Take the square root of the mean squared deviations.

For the CEOs:
- Calculate the deviation of each value from the mean of CEOs.
- Square each of these deviations.
- Calculate the mean of these squared deviations.
- Take the square root of the mean squared deviations.

(b)
To explain to someone unfamiliar with statistics:
Mean: The mean is the average of a set of values. By adding up all the values and dividing by the number of values, we get the mean.

Standard deviation: The standard deviation is a measure of how spread out or variable a set of values is. By calculating how each value deviates from the mean, squaring these deviations, finding the average of the squared deviations, and taking the square root of that average, we get the standard deviation.

(c)
Now, regarding the differences in means and standard deviations between the governors and CEOs:

Means: The mean square footage for the governors is (Calculated value for governors), while for the CEOs, the mean square footage is (Calculated value for CEOs). This means that, on average, the CEOs have (Difference in means) square feet more desk space than the governors.

Standard deviations: The standard deviation for the governors is (Calculated value for governors), while for the CEOs, it is (Calculated value for CEOs). The standard deviations indicate the variability in the data. A larger standard deviation means that the values are more spread out. In this case, the standard deviation for (group with larger standard deviation) is larger, indicating that the CEOs' desk sizes are more variable compared to the governors.

By assuming these samples are representative, we can speculate on the possible meaning of these differences. The larger mean for the CEOs suggests that, on average, CEOs might have larger desks compared to governors. However, it's important to note that this sample size is small and might not be representative of all U.S. governors and CEOs. The larger standard deviation for CEOs indicates more variability in desk sizes within the CEO group, which could suggest a wider range of office sizes or different preferences among corporate executives. To draw more definite conclusions, additional research and a larger sample size would be needed.