2.11

Air quality. Daily air quality is measured by the air quality index (AQI) reported by the Environmental Protection Agency. This index reports the pollution level and what associated health effects might be a concern. The index is calculated for five major air pollutants regulated by the Clean Air Act and takes values from 0 to 300, where a higher value indicates lower air quality. AQI was reported for a sample of 91 days in 2011 in Durham, NC. The relative frequency histogram below shows the distribution of the AQI values on these days.

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a

Estimate the median AQI value of this sample.

# the median is approximately 30.

b

Would you expect the mean AQI value of this sample to be higher or lower than the median? Explain your reasoning.

# Because the AQI relative frequency distribution is skewed right, the mean will be
# influenced by the higher values, resulting in a higher mean than median.

c

Estimate Q1, Q3, and IQR for the distribution.

# Q1 is approximately 15, Q3 is approximately 40, and the IQR, or Q3 - Q1, is approximately 25.

d

Would any of the days in this sample be considered to have an unusually low or high AQI? Explain your reasoning.

# Any outliers would be lower than Q1 - 1.5 * IQR or higher than Q3 + 1.5 * IQR.
# That is, 15 - 1.5 * 25 = -22.5 and 40 + 1.5 * 25 = 77.5.
# Since all data are within these bounds, there aren't any unusual AQI.