Question

describe the distribution and summarize the important features. what is it about running that might account for the shape you see? 11. heart attack stays the histogram shows the lengths of hospital stays (in days) for all the female patients admitted to hospitals in new york during one year with a primary diagnosis of acute myocardial infarction (heart attack). a) from the histogram, would you expect the mean or median to be larger? explain. b) write a few sentences describing this distribution (shape, center, spread, unusual features). c) which summary statistics would you choose to summarize the center and spread in these data? why?

Explanation:

Part (a)

Step1: Analyze Distribution Shape

The histogram is right - skewed (tail on the right, longer stays).

Step2: Recall Mean/Median in Skewness

In a right - skewed distribution, the mean is pulled in the direction of the skew (towards the long tail) while the median is resistant to extreme values. So the mean will be larger than the median.

• Shape: The distribution of hospital stay lengths is right - skewed. Most stays are relatively short (peak around 5 - 10 days), with a long tail of longer stays (some patients stay 15 + days, even up to 40 days).
• Center: Due to right - skewness, the median is a better measure of center, but a typical stay is around the peak (5 - 10 days) before the skew.
• Spread: The data spreads from 0 to 40 days. The right - skew means most of the data is in the lower range (0 - 15 days) with some spread to higher values.
• Unusual Features: There are some patients with very long stays (the long tail), which are outliers or extreme values compared to the majority of short - stay patients.

• Center: Median. The right - skewed distribution has extreme values (long stays) that inflate the mean. The median is resistant to these outliers and better represents the "typical" stay.
• Spread: Interquartile Range (IQR). IQR measures the spread of the middle 50% of data, which is resistant to the extreme values in the right tail (unlike range or standard deviation which are affected by outliers).

Answer:

The mean is expected to be larger. The distribution is right - skewed, and the mean is pulled by the long tail (unusually long hospital stays) while the median is not affected as much by these extreme values.

Part (b)