3. Describing Data Numerically

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 $x$ = $140$?

Interpreting the Coefficient of Determination

In Exercises 5–8, use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables.

Times of Taxi Rides and Tips r = 0.298 (x = time in minutes, y = the amount of tip in dollars)

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

In Exercises 1 and 2, use the following wait times (minutes) at 10:00 AM for the Tower of Terror ride at Disney World (from Data Set 33 “Disney World Wait Times” in Appendix B).

35 35 20 50 95 75 45 50 30 35 30 30

d. Find the variance.

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?