3. Describing Data Numerically

According to the empirical rule for a normal distribution, $99.7\%$ of $7$-year-old children are between which of the following heights if the mean height is $48$ inches and the standard deviation is $2$ inches?

If the unit of a dataset is $\mathrm{meters}$, the unit for population variance would be

The standard deviation of the distribution of sample means is $\frac{\sigma }{\sqrt{n}}$.

If the standard deviation for a set of data is $0$, what does this indicate about the data values?

Given the data set $5,7,9,10,14$, what is the value of the standard error of the mean for this sample?

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

Which term represents the number of standard deviations an observation is from the $\mathrm{mean}$?

$\mathrm{Standard deviation}$ is a direct measure of which of the following in a data set?

Shifting Data Sample annual salaries (in thousands of dollars) for employees at a company are listed.

40   35   49   53   38   39   40

37   49   34   38   43   47   35

c. Each employee in the sample takes a pay cut of \$2000 from their original salary. Find the sample mean and the sample standard deviation for the revised data set.

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. Which histogram depicts a higher $\mathrm{standard\; deviation}$?

Which of the following is not a property of the $s \left(\mathrm{standard\; deviation}\right)$?

If the standard deviation for a set of data is $0$, what does this indicate about the data values?

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

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