Daily air quality is measured by the air quality Index (AQI) reported by the Env
ID: 3201537 • Letter: D
Question
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. Estimate the median class and median AQI value of this sample. Would you expect the mean AQI value of this sample to be higher or lower than the median? Explain your reasoning. Estimate Q1 and Q3 values. Estimate the IQR for the distribution.Explanation / Answer
1:
Median is data value that has 50% data values less than from it. Since cumulative frequency for the bar corresponding to 25 to 30 is 0.02+0.05+0.2+0.07+.2 = 0.54 so median lie in the interval 25 to 30. Median AIQ is (30+25) /2 = 27.5
and median class is 25 to 30.
2:
Distribution is skewed to right slightly so mean should be higher than median.
3;
Q1 is the data value that has 25% area less than from it. Since cumulative frequency for the bar corresponding to 15 to 20 is 0.02+0.05+0.2 = 0.27 so Q1 lie in the interval 15 to 20. First quratile AIQ is (20+15) /2 = 17.5.
Q3 is the data value that has 75% area less than from it. Since cumulative frequency for the bar corresponding to 35 to 40 is 0.02+0.05+0.2+0.07+0.2+0.15+0.07 = 0.76 so Q3 lie in the interval 35 to 40. Third quratile AIQ is (40+35) /2 = 37.5.
4:
IQR = Q3 - Q1 = 37.5 - 17.5 = 20
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