Chapter 1.3, Problem 100E

(a)

To determine

To explain: the distribution which has a more symmetrical shape

Answer to Problem 100E

The distribution for female doctors is roughly symmetric.

Explanation of Solution

Given:

	$\overline{X}$	$s_x$	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

Calculation:

FEMALE:

Mean: $\overline{x}=19.1$

Median: $M=18.5$

The mean and median are very close together and thus the distribution for female doctors is roughly symmetric.

MALE:

Mean: $\overline{x}=41.333$

Median: $M=34$

The mean and median are far apart and thus the distribution for male doctors is not roughly symmetric.

Conclusion:

Therefore, the distribution for female doctors is roughly symmetric.

(b)

To determine

To explain: why the IQRs of the distributions

Answer to Problem 100E

The IQR is not influenced by outliers, while the standard deviation is influenced by outliers.

Explanation of Solution

The IQR is not influenced by outliers, while the standard deviation is influenced by outliers.

Thus one of these two distributions (the distribution of the female doctors) will most likely contain outliers which affect the value of the standard deviation.

(c)

To determine

To find:whether males perform more C-sections or not

Answer to Problem 100E

The male doctors appear to perform more C-sections

Explanation of Solution

Calculation:

The male doctors appear to perform more C-sections than the female doctors, because the mean $\overline{x}$ , the minimum, 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.