3. Describing Data Numerically

Which of the following values can the variance of a dataset never be?

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 $\mathrm{standard} \mathrm{deviation}$?

Given the population data set $2,0,1,9$, what is the variance of this population?

Given a population with mean $\mu$ = $65$ and standard deviation $\sigma$ = $4$, what is the z-score of a value $x$ = $73$?

Given the sample data $8$, $6$, $2$, $8$, what is the variance of the sample?

Which of the following correctly represents the formula for the population standard deviation?

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

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

Which of the following is true for the quantity $\sqrt{x-\mu }$?

Given four normal curves with the same mean ($\mu$) but different spreads, which one of the following curves has the largest standard deviation ($\sigma$)?

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

Which of the following is not a property of the $standarddeviation$?

Suppose a graph shows a normal distribution of data with a mean of $\mu =5$ and the data points are most densely clustered between $3.5$ and $6.5$. What is the standard deviation $\sigma$ of the data?

Given a population with mean $\mu$ = $100$ and standard deviation $\sigma$ = $20$, what is the z-score of a value $x$ = $140$?

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