Question

A study in Switzerland examined the number of cesarean sections (surgical deliveries of babies) performed in a year by samples of male and female doctors. Here are the summary statistics for the two distributions:

Based on the computer output, which distribution has a more symmetrical shape? Why?
A)The distribution of female doctors is more symmetric because the mean and median are closer together than the mean and median of the distribution of male doctors.
B)It is impossible to tell without seeing a graph of the data.
C)The distribution of female doctors is more symmetric because the IQR for the distribution of female doctors is smaller than the IQR for the distribution of male doctors.
D)The distribution of male doctors is more symmetric because the standard deviation and range are both larger than the distribution of female doctors. This increased variability must mean that their distribution is more symmetric.
E)Male and Female distributions are approximately equal in symmetry because for each distribution the standard deviation is approximately half of the mean.

Answer 1

Based on principles of a symmetrical distribution, where the mean and median are identical, Option A is the most suitable choice as it indicates the distribution of female doctors is more symmetric because the mean and median are closer together.

option a is the correct

Step-by-step explanation:

To determine which distribution has a more symmetrical shape, consider the properties of a symmetrical distribution. In a perfectly symmetrical distribution, the mean and the median are identical, signifying that the distribution is even on both sides of this central point. This occurs because the mean, median, and mode coincide at the peak of the distribution if it is symmetrical, and they do not show any signs of the data being pulled or skewed in one direction.

An important concept to remember is that the closer the mean and median are to each other, the more likely the distribution is to be symmetrical. Skewness is indicated by a significant difference between these central measures. A right-skewed (positive skew) distribution will have the mean greater than the median, and for a left-skewed (negative skew), the median will be higher than the mean.

Let's consider the answer choices in the context of these principles:

• Option A suggests that the female doctors' distribution is more symmetric because the mean and median are closer together, which aligns with the principles of a symmetrical distribution. Without exact figures, however, it is hard to confirm this completely.
• Option B suggests it is impossible to tell without seeing a graph of the data. Visual representation can indeed provide a clear indication of symmetry, yet the relationship between the mean and median can also be a strong indicator.
• Option C mentions the Interquartile Range (IQR), but while a smaller IQR can indicate less variability, it is not directly indicative of symmetry.
• Option D incorrectly associates larger standard deviation and range with higher symmetry, which is not necessarily true, as these can exist in both symmetrical and skewed distributions.
• Option E makes a general statement about standard deviation being about half of the mean for both distributions; however, this ratio does not directly relate to symmetry.

The most suitable option that follows the principles mentioned above is Option A, which indicates that the distribution of female doctors is more symmetric because the mean and median are closer together.