Questions: The results of rolling a six-sided die 30 times are shown. Construct a frequency distribution and a frequency histogram for the data set using 6 classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, or positively skewed. Determine what are the six classes. A. The classes are the weighted means of each die being rolled. B. The frequency of each die being rolled. C. The frequency multiplied by the midpoint, xf , in the equation x̄ = (sum(xf))/n. D. The possible dice rolls, therefore 1,2,3,4,5,6.

The results of rolling a six-sided die 30 times are shown. Construct a frequency distribution and a frequency histogram for the data set using 6 classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, or positively skewed.

Determine what are the six classes.
A. The classes are the weighted means of each die being rolled.
B. The frequency of each die being rolled.
C. The frequency multiplied by the midpoint, xf , in the equation x̄ = (sum(xf))/n.
D. The possible dice rolls, therefore 1,2,3,4,5,6.

Transcript text: The results of rolling a six-sided die 30 times are shown. Construct a frequency distribution and a frequency histogram for the data set using 6 classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, or positively skewed. Determine what are the six classes. A. The classes are the weighted means of each die being rolled. B. The frequency of each die being rolled. C. The frequency multiplied by the midpoint, xf , in the equation $\overline{\mathrm{x}}=\frac{\sum(\mathrm{xf})}{\mathrm{n}}$. D. The possible dice rolls, therefore $1,2,3,4,5,6$.

Solution

Solution Steps

Step 1: Identify the Classes

The six classes for the frequency distribution are the possible outcomes of rolling a six-sided die. These outcomes are $1, 2, 3, 4, 5, 6$. Therefore, the correct answer is D. The possible dice rolls, therefore $1,2,3,4,5,6$.

Step 2: Construct the Frequency Distribution

Count the frequency of each outcome in the given data set:

$1$ appears $5$ times.
$2$ appears $6$ times.
$3$ appears $6$ times.
$4$ appears $4$ times.
$5$ appears $4$ times.
$6$ appears $5$ times.

The frequency distribution is as follows: \[ \begin{tabular}{|c|c|} \hline \text{Outcome} & \text{Frequency} \\ \hline 1 & 5 \\ 2 & 6 \\ 3 & 6 \\ 4 & 4 \\ 5 & 4 \\ 6 & 5 \\ \hline \end{tabular} \]

Step 3: Construct the Frequency Histogram

Using the frequency distribution, create a histogram with the outcomes $1, 2, 3, 4, 5, 6$ on the x-axis and their corresponding frequencies on the y-axis. Each bar represents the frequency of each outcome.

Step 4: Describe the Shape of the Histogram

The histogram is uniform because the frequencies of the outcomes are roughly equal, with no significant skewness or asymmetry.