Question

1. -/10 points

a survey of 15 large cities noted the average weekly commute times, in hours, of the residents of each city. the results are recorded in the table below.
find the mean and sample standard deviation of these data. round to the nearest hundredth.
mean
sample standard deviation
resources
read it

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}$ of a sample is $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$.
First, find the sum of the data values:

$$
LATEXBLOCK0
$$

Since \(n = 15\), the mean \(\bar{x}=\frac{61.1}{15}\approx4.07\)

Step2: Calculate the sample standard deviation

The formula for the sample standard deviation \(s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}\)
First, calculate \((x_{i}-\bar{x})^{2}\) for each \(x_{i}\):

$$
LATEXBLOCK1
$$

Then find the sum of \((x_{i}-\bar{x})^{2}\):

$$
LATEXBLOCK2
$$

Since \(n = 15\), then \(n-1=14\)
\(s=\sqrt{\frac{18.7495}{14}}\approx\sqrt{1.33925}\approx1.16\)

Answer:

mean: \(4.07\)
sample standard deviation: \(1.16\)