Question

1. find the variance and standard deviation for the seven states with the most covered bridges: oregon: 106 vermont: 121 pennsylvania: 347 indiana: 152 new hampshire: 45 ohio: 234 new jersey: 35
2. find the variance and standard deviation of the heights of five tallest skyscrapers in the united states: sears tower (willis building): 1450 feet empire state building: 1250 feet one world trade center: 1776 feet trump tower: 1388 feet 2 world trade center: 1340 feet
3. find the variance and standard deviation of the scores on the most recent reading test: 7.7, 7.4, 7.1, 7.7, 7.2, 7.3, and 7.9
4. find the variance and standard deviation of the highest temperatures recorded in eight specific states: 112, 100, 127, 120, 134, 118, 105, and 110.

Explanation:

Step1: Calculate the mean

For the first - set of data (covered bridges):
The data set is \(x = \{106,121,347,152,45,234,35\}\).
The mean \(\bar{x}=\frac{106 + 121+347+152+45+234+35}{7}=\frac{1030}{7}\approx147.14\)

Step2: Calculate the squared - differences

\((106 - 147.14)^2=( - 41.14)^2 = 1702.50\)
\((121-147.14)^2=( - 26.14)^2 = 683.30\)
\((347-147.14)^2=(199.86)^2 = 39944.02\)
\((152 - 147.14)^2=(4.86)^2 = 23.62\)
\((45-147.14)^2=( - 102.14)^2 = 10432.58\)
\((234-147.14)^2=(86.86)^2 = 7542.66\)
\((35-147.14)^2=( - 112.14)^2 = 12574.98\)

Step3: Calculate the variance

The variance \(s^{2}=\frac{1702.50+683.30 + 39944.02+23.62+10432.58+7542.66+12574.98}{7 - 1}\)
\(s^{2}=\frac{73803.66}{6}\approx12300.61\)

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{12300.61}\approx110.91\)

Answer:

Variance: approximately \(12300.61\), Standard deviation: approximately \(110.91\)