3. Describing Data Numerically

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?

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?