3. Describing Data Numerically

As the standard deviation $\sigma$ decreases, what happens to the graph of the normal distribution curve?

Which of the following values can never be the numerical value of the standard deviation of a data set?

Why is the $standard deviation$ used more frequently than the $variance$ when describing the spread of a data set?

Which of the following is a good point estimator for the population variance?

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

Suppose you have two histograms, Histogram A and Histogram B, each representing the distribution of exam scores for two different classes. Histogram A shows scores tightly clustered around the $\mathrm{mean}$, while Histogram B shows scores spread out over a wider range. Based on this information, which histogram depicts a higher $\mathrm{standard\; deviation}$?

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

Given the population data set consisting of a single value $3$, what is the standard deviation of the population?

If the standard deviation of a dataset is $0.5$, what is the variance of the data?

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

Which of the following symbols identifies the population standard deviation?

Which characteristic must be known about a data set before the empirical rule can be applied?

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

Standard deviation is commonly used to measure which type of risk in a data set? $\sigma$