3. Describing Data Numerically

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? $\sigma$

For a given dataset, the unit for the population standard deviation would be:

Which of the following is true regarding the standard error of the estimate ($\mathrm{SE}$)?

Which of the following statements about the standard deviation of a dataset is correct?

Given the sample data set consisting of a single value $8$, what is the variance of the sample?

Graphical Analysis In Exercises 21–24, you are asked to compare three data sets.

(c) Estimate the sample standard deviations. Then determine how close each of your estimates is by finding the sample standard deviations.

i.

ii.

iii.

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 $standard deviation$?

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?

$Which\; of\; the\; following\; groups\; of\; scores\; would\; have\; the\; smallest\; standard\; deviation?$

A sample of $n=5$ scores has a mean of $m=20$ and a sample variance of $s^2=4$. What is the sample standard deviation?

Given the data set $4,8,12,24$, what is the standard deviation of the data (rounded to two decimal places)?

In statistics, which symbol is commonly used to represent the standard error of the sample mean $m$?