How Democratic is Georgia? County-by-county results are shown for a recent elect

Question

How Democratic is Georgia? County-by-county results are shown for a recent election. For your convenience, the data have been sorted in increasing order (Source: County and City Data Book, 12th edition, U.S. Census Bureau). Percentage of Democratic Vote by Counties in Georgia 31 33 34 34 35 35 35 36 38 38 38 39 40 40 40 40 41 41 41 41 41 41 41 42 42 43 44 44 44 45 45 46 46 46 46 47 48 49 49 49 49 50 51 52 52 53 53 53 53 53 55 56 56 57 57 59 62 66 66 68 (b) Find the interquartile range.

Then estimate the mean and sample standard deviation using the frequency table. (Round x to one decimal place, and round s to two decimal places.)

x

s

Compute a 75% Chebyshev interval centered about the mean. (Round your answers to two decimal places.)

Lower limit

Upper limit

(d) If you have a statistical calculator or computer, use it to find the actual sample mean and sample standard deviation. Otherwise, use the values x = 2769 and x2 = 132,179 to compute the sample mean and sample standard deviation. (Round your answers to two decimal places.)

x

s

Explanation / Answer

Here, Number of observations = 59

Interquartile Range = Third Quartile(Q3) - First Quartile (Q1)

Q1 = (N+1)/4 observation = 15th observation = 40

Q3 = (3/4)*(N+1) observation = 45th observation = 52

Now, Interquartile Range = 52-45 = 7

I have constructed below the frequency table. X denotes the occurence of an observation and f denotes the frequency of the occurence of that particular observation in the data.

2713

Mean = 2713/59 = 45.98 = 46 approximately

x f fx 31 1 31 33 1 33 34 2 68 35 3 105 36 1 36 38 3 114 39 1 39 40 4 160 41 7 287 42 2 84 43 1 43 44 3 132 45 2 90 46 4 184 47 1 47 48 1 48 49 4 196 50 1 50 51 1 51 52 2 104 53 5 265 55 1 55 56 1 56 57 2 114 59 1 59 62 1 62 66 2 132 68 1 68 Total 59

2713

Mean = 2713/59 = 45.98 = 46 approximately

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