Q 100. - The Practice of Statistics for AP

Question

C-sections Do male doctors perform more cesarean sections (C-sections) than female doctors? A study in Switzerland examined the number of cesarean sections (surgical deliveries of babies) performed in a $100$. Section $1.3$ Describing Quantitative Data with Numbers $73$ year by samples of male and female doctors. Here are summary statistics for the two distributions: 

(a) Based on the computer output, which distribution would you guess has a more symmetrical shape? Explain. 

(b) Explain how the IQRs of these two distributions can be so similar even though the standard deviations are quite different. 

(c) Does it appear that males perform more C-sections? Justify your answer 

Step-by-Step Solution

Answer

Part (a) The distribution for female doctors is roughly symmetric

Part (b) The IQR is not influenced by outliers, while the standard deviation is influenced by outliers.

Part (c) The male doctors appear to perform more C-sections.

Step 1: Given information

A Swiss study looked at how many cesarean sections (baby births via surgery) were performed per$100$The summary statistics for the two distribution is given in the below table: 

	$\overline{x}$	$s_x$	$Min$	$Q_1$	$M$	$Q_3$	Max	IQR
Male doctors	41.333	20.607	20	27	34	50	86	23
Female doctors	19.1	10.126	5	10	18.5	29	33	19

Part (a) Step 2: Concept

A statistical graph or chart is a visual representation of statistical data in graphical form.

Part (a) Step 3: calculation

FEMALE: 

Mean: $\overline{x} = 19.1$

Median: $M=18.5$

Because the mean and median are so close, the distribution of female doctors is essentially symmetric.

MALE:

Mean: $\overline{x}=41.333$

Median: $M=34$

Because the mean and median are so far off, the male doctor distribution is not generally symmetric. Therefore, the distribution for female doctors is roughly symmetric.

Part (b) Step 1: Explanation

Outliers have no effect on the IQR, but they do have an impact on the standard deviation. As a result, one of these two distributions (the distribution of female doctors) will almost certainly have outliers that affect the standard deviation figure.

Part (c) Step 1: Explanation

Because the mean x, the lowest, the first quartile $Q_1$, the median $M$, the third quartile $Q_3$, and the maximum are all larger for male doctors than for female doctors, it appears that male doctors execute more C-sections.