3. Describing Data Numerically

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?

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?

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 $\mathrm{standard\; deviation}$?

Given the data set $1,2,4,5$, what is the variance of the data?

Suppose the weights of a group of students are normally distributed with a mean of $\mu =70 \mathrm{kg}$ and a standard deviation of $\sigma =5 \mathrm{kg}$. Which of the following weights are within $2$ standard deviations of the mean? Select three options.

If the sample variance of hourly wages is $10$, what is the sample standard deviation?

According to the range rule of thumb, the standard deviation of a data set can be roughly estimated as $\frac{\mathrm{Range}}{4}$.

Larger values of the standard deviation result in a normal curve that is: $\sigma$

In the calculation of a $z$-score, what does the denominator of the test statistic measure?

According to the empirical rule, what proportion of bond mutual funds' returns are expected to fall within $1$ standard deviation of the mean if the returns are approximately normally distributed?