3. Describing Data Numerically

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 $m$?

As the mean $\mu$ increases in a normal distribution, what happens to the graph of the normal curve?

Which formula should you use to calculate the variance and which formula should you use to calculate the standard deviation of a sample of $n$ observations $x_1$, $x_2$, ..., $x_n$?

Which of the following is true about $\mathrm{variance}$?

Which of the following best describes the relationship between $\mathrm{variance}$ and $\mathrm{standard\; deviation}$ for a data set?

Which three quantities are required to calculate the variance of a data set?

Which of the following is the correct formula for the population variance?

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