1. To calculate the variance and standard deviation for the five states with the most covered bridges, we first need to find the mean of the data set. The mean is (106 + 121 + 152 + 234 + 347) / 5 = 192.
The variance is calculated as follows:
[(106 - 192)^2 + (121 - 192)^2 + (152 - 192)^2 + (234 - 192)^2 + (347 - 192)^2] / 5
= [8,464 + 4,410 + 961 + 4,524 + 22,729] / 5
= 8,618.4
The standard deviation is the square root of the variance:
√8,618.4 = 92.8
2. To calculate the variance and standard deviation of the heights of the five tallest skyscrapers in the United States, we first need to find the mean of the data set. The mean is (1450 + 1250 + 1776 + 1388 + 1340) / 5 = 1440.8.
The variance is calculated as follows:
[(1450 - 1440.8)^2 + (1250 - 1440.8)^2 + (1776 - 1440.8)^2 + (1388 - 1440.8)^2 + (1340 - 1440.8)^2] / 5
= [85.64 + 191,636.64 + 1,955,298.24 + 3,489.44 + 10,411.24] / 5
= 231,564
The standard deviation is the square root of the variance:
√231,564 = 481.1
3. To calculate the variance and standard deviation of the scores on the most recent reading test, we first need to find the mean of the data set. The mean is (7.7 + 7.4 + 7.3 + 7.9) / 4 = 7.575.
The variance is calculated as follows:
[(7.7 - 7.575)^2 + (7.4 - 7.575)^2 + (7.3 - 7.575)^2 + (7.9 - 7.575)^2] / 4
= [0.015625 + 0.076225 + 0