Carbon monoxide is a gas that is highly toxic Researchers su

Carbon monoxide is a gas that is highly toxic. Researchers suspect that downtown may have a higher concentration of carbon monoxide than the suburbs. The data is collected in ppm (parts per million) over a fixed period of time from a downtown location and a suburb location. Below, we provide some descriptive statistics for both locations, i.e. downtown and suburb. (PICTURE ATTACHED)

> summary(Downtown) Min. 1st Qu. Median Mean 3rd Qu. Max. 8.60 11.10 12.30 11.75 12.90 13.80

> summary(Suburb) Min. 1st Qu. Median Mean 3rd Qu. Max. 7.800 8.700 9.600 9.662 10.270 12.300

(a) For each location (i.e. downtown and suburb) describe its distribution in shape, central tendency, and dispersion. (b) For each variable, are there any outliers in the sample? (Explain) (c) Which location has the highest concentration of carbon monoxide? (Explain) (d) Which location has a higher central tendency regarding the concentration of Carbon monoxide? (Explain) (e) Are the data collected from downtown more dispersed than the data collected from the suburb? (Explain)

Histogram of Downtown Histogram of Suburb 8 9 10 11131 7 8 91011213 Downtown Suburb Downtown Suburb

Solution

(a)

The distribution of carbon mono-oxide concentration in downtown can be clearly observed from histogram to have slightly shifted towards right.The shape almost resembles the normal distribution.

The corresponding distribution in suburb can be observed to be alightly shifted towards the left. Here again the shape resembles to that of a normal distribution.

Also from the interquartile range we can say that the dispersion is less in case of suburbs as compared to that of Downtown.

(b)

For Downtown:

Interquartile range ,IQR = 12.90 - 11.10 = 1.80

1.5 IQR = 1.5*1.80 = 2.70

Lower limit for outliers = first quartile - 1.5IQR = 11.10 - 2.70 = 8.40

Upper limit for outliers = Third quartile + 1.5IQR = 12.90 + 2.70 = 15.60

Since maximum and minimum are within limits, there are no outliers for this distribution.

For Suburbs:

Interquartile range ,IQR = 10.270 - 8.700 = 1.57

1.5IQR = 2.355

Lower limit for outliers = first quartile - 1.5IQR = 8.700 - 2.355 =6.345

Upper limit for outliers = Third quartile + 1.5IQR = 10.270 + 2.355 = 12.625

In this case too maximum and minimum lie within limits, thus the distribution must have no outliers .

(c)

From the comparision of maximum of both distribution we can see that Downtown has highest concentration of carbon mono-oxide.

(d)

From the comparision of mean and median of both distributions , we can clearly state that Downtown has higher central tendence regarding the concentration of Carbon Monoxide.

(d)

From the interquartile range comparision we can say that the downtown data is more dispersed than the data collected from the suburb.