3. Describing Data Numerically

Suppose you are shown four histograms, each representing a different data set with the same mean $\mu$. Which data set is most likely to have the smallest standard deviation $\sigma$?

A population of $n=10$ scores has mean $\mu =21$ and standard deviation $\sigma =3$. What is the population variance?

Given the data set $65,75,100,130$, what is the standard deviation of the data? Round your answer to the nearest whole number.

Which of the following best describes the usefulness of the $standarddeviation$ in statistics?

If a set of data has a standard deviation of $0$, which of the following must be true about the data?

For a sample mean, which combination of sample standard deviation $s$ and sample size $n$ will produce the largest value for the standard error $\frac{s}{\sqrt{n}}$?

In the context of a statistical model, which measure best represents the typical size of a prediction error for this model?

Which of the following statements is true of the $standarddeviation$?

If a dataset has a sample variance of $6$, what is the sample standard deviation?

Given the sample data set: $7$, what is the standard deviation of this sample?

Which of the following best explains why the $\mathrm{range}$ is less desirable than the $\mathrm{standard\; deviation}$ as a measure of dispersion?

For a bell-shaped data set, approximately what percentage of the data will be in the interval $\mu -\sigma$ to $\mu +\sigma$?

Which one of the following is the positive square root of the $\mathrm{variance}$?

In the context of statistics, how can the $s=\sqrt{\frac{\sum {x-\mu }^2}{n}}$ (standard deviation) be used to specify uncertainty in a set of measurements?

According to the range rule of thumb, the standard deviation of a data set can be roughly estimated as which of the following expressions?