Question

the sample data provided contains numbers of injuries due to distracted driving for the past 15 months for a certain town. find the standard deviation for the sample set of data. injuries due to distracted driving per month 9,074 8,611 6,922 8,065 10,457 7,551 6,985 9,316 5,292 4,299 6,132 9,442 9,570 12,080 9,433

Explanation:

Step1: Calculate the mean

First, sum up all the data values:

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The number of data points \(n = 15\). The mean \(\bar{x}=\frac{132201}{15}=8813.4\)

Step2: Calculate the squared differences from the mean

For each data point \(x_i\), calculate \((x_i-\bar{x})^2\). For example, for \(x_1 = 9074\): \((9074 - 8813.4)^2=(260.6)^2 = 67912.36\)
After calculating for all \(x_i\) and summing them up: \(\sum_{i = 1}^{15}(x_i-\bar{x})^2=63499797.6\)

Step3: Calculate the sample variance

The sample variance \(s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}=\frac{63499797.6}{14}\approx4535700\)

Step4: Calculate the sample standard deviation

The sample standard deviation \(s=\sqrt{s^2}=\sqrt{4535700}\approx2134.86\)

Answer:

2,134.86