Question

The following table shows death rates due to chronic obstructive pulmonary disease among adult men in the Southern states and Mountain states in 2005. Use this data to compare death rates due to this disease in the two regions of the country.

Death Rates Due to Chronic Obstructive Pulmonary Disease Among Adult Men by Region: 2005 (Deaths per 100,000)

Southern Region		Mountain Region
Washington, DC	41.4	Utah	64.5
Maryland	56.8	Idaho	98.1
Georgia	87.5	New Mexico	82.0
Virginia	73.5	Colorado	95.6
South Carolina	86.4	Wyoming	103.6
North Carolina	94.0	Arizona	74.1
Delaware	77.3	Nevada	95.2
Florida	66.3	Montana	98.1
West Virginia	113.6

Source: National Vital Statistics System, 2005

www.cdc.gov/mmwr/preview/mmwrhtml/mm5745a4.htm

a.   Which region had the highest mean death rate from chronic obstructive pulmonary disease? Show calculations.

b.   Calculate the median death rate due to chronic obstructive pulmonary disease in each region. Show calculations and write an interpretation for the median in each case.

c.   Describe the shape of the distribution in the Mountain states, and explain how you arrived at your description.

Answer 1

a) Mean = Sum of all the deaths / Total no. of Region

For Southern region = 41.4+56.8+87.5+73.5+86.4+94+77.3+66.3+113.6 / 9 = 77.42

For Mountain region = 64.5+98.1+82+95.6+103.6+74.1+95.2+98.1/ 8 = 88.9  

So highest mean death rate is for the mountain region

b) Median = To find the median, we arrange the observations in order from smallest to largest value. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values.

Arranging both in increasing order

Southern	Mountain
41.4	64.5
56.8	74.1
66.3	82
73.5	95.2
77.3	95.6
86.4	98.1
87.5	98.1
94	103.6
113.6

  

For Southern region = The 5th term is 77.3 so Median = 77.3

The median is almost equal to the mean, in this case, we can say that the data is not skewed. The data is symmetrical

For Mountain region = 4th + 5th / 2 = (95.2 + 95.6) / 2 = 95.4

The median is way too higher than the mean, there is a large difference between mean and median. This data is highly skewed.

c) The shape of the distribution

The graph is increasing where there is a sharp increase at first but then almost constant change at the end.