3. Describing Data Numerically

If a distribution has zero variance, which of the following statements is true about the data values? $\mathrm{Var}\left(X\right)=0$

According to the empirical rule, what proportion of bond mutual funds are expected to have returns within $1^{\sigma }$ of the mean if the returns are approximately normally distributed?

Suppose you have two histograms, $A$ and $B$, each representing the distribution of exam scores for two different classes. Histogram $A$ shows scores tightly clustered around the mean, while Histogram $B$ shows scores spread out over a wider range. Which histogram depicts a higher standard deviation?

In statistics, does the value of the $\mathrm{standard\; deviation}$ of a data set depend on the value of the $\mathrm{mean}$ of that data set?

Why is the $standard deviation$ generally considered a better measure of variation than the $range$?

Which of the following symbols identifies the sample standard deviation?

What is the relationship between the $\mathrm{variance}$ and the $\mathrm{standard\; deviation}$ for a sample data set?

Which of the following is key to generating a bell curve in statistics?

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?