# How Democratic is Georgia County by-county results are shown for a recent election. For your convenience,...

How Democratic is Georgia County by-county results are shown for a recent election. For your convenience, the dates have been sorted in increasing order (Source County and City Data Hook, 12th edition, U.S. Census Bureau). Percentage of Democratic Vote by Counties in George 31 33 34 34 35 35 35 36 38 40 41 41 41 41 41 41 41 45 46 46 46 46 47 48 49 49 53 53 53 53 53 55 56 56 57 57 (a) Select the box-and-whisker plot of the data
10 20 30 40 50 60 70 0 0 (b) Find the interquartile range, (c) Make a frequency table using five classes, class 31-38 39-46 47.54 55-62 63-70 Then estimate the mean and sample standard deviation using the frequency table. (Round x to one decimal place, and rounds to two decimal places.)
Then estimate the mean and sample standard deviation using the frequency table. (Round X to one decimal place, and rounds to two decimal places. 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, set to find the actual sample mean and sample standard deviation Otherwise use the values Ex-2760 and Ex? = 132,179 compute the sample mean and sample standard deviation, (Round your answers to two decimal places

a) Box-and-whisker plot: plot 1st

b)

5 point summary:

Minimum = 31

First quartile, Q1 = 40

Median =45

Third quartile, Q3 = 52.5

Maximum = 68

Interquartile range, IQR = Q3 - Q1 = 52.5 - 40 = 12.5

c)

 Class interval Frequency 31 - 38 11 39 - 46 24 47 - 54 15 55 - 62 7 63 - 70 3 Total 60
 Class interval Midpoint, x Frequency, f fx fx² 31 - 38 34.5 11 379.5 13092.75 39 - 46 42.5 24 1020 43350 47 - 54 50.5 15 757.5 38253.75 55 - 62 58.5 7 409.5 23955.75 63 - 70 66.5 3 199.5 13266.75 Total 60 2766 131919

Mean, x̅ = ∑fx / n = 2766/60 = 46.1

Standard deviation, s = √((∑fx² - (∑fx)²/n)/(n-1)) = √((131919 - 2766²/60)/(60- 1))

= 8.6420 = 8.64

----

Chebyshev's theorem states that the proportion or percentage of any data set that lies within k standard deviation of the mean where k is any positive integer greater than 1 is at least 1 – 1/k^2.

0.75 = 1-1/k²

1/k² = 1 - 0.75

k² = 1/0.25

k = 2

75% Chebyshev interval centered about the mean.

Lower limit = x̅ - 2*s = 46.1 - 2*8.64 = 28.82

Upper imit = x̅ + 2*s = 46.1 + 2*8.64 = 63.38

d)

∑x = 2769

∑x² = 132179

n = 60

Mean, x̅ = Ʃx/n = 2769/60 = 46.15

Standard deviation, s = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(132179-(2769)²/60)/(60-1)]

= 8.6256 = 8.63

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