Question

1. find the standard deviation of the sample for the five states with the most covered bridges:

oregon: 106
vermont: 121
indiana: 152
ohio: 234
pennsylvania: 347
round to the nearest tenth. (one decimal)

Explanation:

Step1: Calculate the mean ($\bar{x}$)

First, find the sum of the data values: \(106 + 121 + 152 + 224 + 347 = 950\)
There are \(n = 5\) data points, so the mean is \(\bar{x}=\frac{950}{5}=190\)

Step2: Calculate the squared differences from the mean

For each data point \(x_i\), calculate \((x_i - \bar{x})^2\):

• For \(106\): \((106 - 190)^2=(-84)^2 = 7056\)
• For \(121\): \((121 - 190)^2=(-69)^2 = 4761\)
• For \(152\): \((152 - 190)^2=(-38)^2 = 1444\)
• For \(224\): \((224 - 190)^2=(34)^2 = 1156\)
• For \(347\): \((347 - 190)^2=(157)^2 = 24649\)

Step3: Calculate the sum of squared differences

Sum these squared differences: \(7056+4761 + 1444+1156+24649 = 39066\)

Step4: Calculate the sample variance ($s^2$)

The sample variance is \(\frac{\sum(x_i - \bar{x})^2}{n - 1}\), so \(s^2=\frac{39066}{5 - 1}=\frac{39066}{4}=9766.5\)

Step5: Calculate the sample standard deviation ($s$)

Take the square root of the variance: \(s=\sqrt{9766.5}\approx98.8\)

Answer:

\(98.8\)