Question

a contractor records the areas, in square feet, of several houses in a neighborhood to determine data about the neighborhood. which formula should be used to calculate the standard deviation?
s^{2}=\frac{(x_{1}-overline{x})^{2}+(x_{2}-overline{x})^{2}+cdots+(x_{n}-overline{x})^{2}}{n - 1}
s=sqrt{\frac{(x_{1}-overline{x})^{2}+(x_{2}-overline{x})^{2}+cdots+(x_{n}-overline{x})^{2}}{n - 1}}
sigma^{2}=\frac{(x_{1}-mu)^{2}+(x_{2}-mu)^{2}+cdots+(x_{n}-mu)^{2}}{n}
sigma=sqrt{\frac{(x_{1}-mu)^{2}+(x_{2}-mu)^{2}+cdots+(x_{n}-mu)^{2}}{n}}
why does the formula use “n - 1” in the denominator?
the data is a sample and is expected to be more dispersed from the mean.
the data is a sample and is expected to be less dispersed from the mean.
the data is a population and is expected to be more dispersed from the mean.
the data is a population and is expected to be less dispersed from the mean.
done

Explanation:

Step1: Identify data type

The contractor records areas of several houses, which is a sample of all houses in the neighborhood.

Step2: Understand standard - deviation formula

When dealing with a sample, we use $n - 1$ in the denominator of the standard - deviation formula to get an unbiased estimator. A sample is expected to be more dispersed from the mean compared to the population.

Answer:

The data is a sample and is expected to be more dispersed from the mean.