Questions: For the given data, construct a frequency distribution and frequency histogram of the data using five classes. Describe the shape of the histogram as symmetric, uniform, skewed left, or skewed right. Data set: California Pick Three Lottery 3 6 7 6 0 6 1 7 8 4 1 5 7 5 9 1 5 3 9 9 2 2 3 0 8 8 4 0 2 4 A. skewed left B. uniform C. skewed right D. symmetric

Solution Steps

To construct a frequency distribution and frequency histogram, we need to:

1. Determine the range of the data.
2. Divide the range into five equal classes.
3. Count the frequency of data points in each class.
4. Plot the histogram using the frequency distribution.
5. Analyze the shape of the histogram.

First, we need to organize the given data set:

\[ \{3, 6, 7, 6, 0, 6, 1, 7, 8, 4, 1, 5, 7, 5, 9, 1, 5, 3, 9, 9, 2, 2, 3, 0, 8, 8, 4, 0, 2, 4\} \]

To construct a frequency distribution with five classes, we first determine the range of the data:

\[ \text{Range} = \text{Maximum value} - \text{Minimum value} = 9 - 0 = 9 \]

Next, we calculate the class width. Since we need five classes, we divide the range by the number of classes and round up if necessary:

\[ \text{Class width} = \frac{\text{Range}}{\text{Number of classes}} = \frac{9}{5} = 1.8 \approx 2 \]

We create five classes with the calculated class width:

1. \(0 - 1\)
2. \(2 - 3\)
3. \(4 - 5\)
4. \(6 - 7\)
5. \(8 - 9\)

We tally the frequencies for each class:

\[ \begin{array}{|c|c|} \hline \text{Class} & \text{Frequency} \\ \hline 0 - 1 & 6 \\ 2 - 3 & 6 \\ 4 - 5 & 6 \\ 6 - 7 & 5 \\ 8 - 9 & 7 \\ \hline \end{array} \]

We now construct the frequency histogram based on the frequency distribution:

\[ \begin{array}{c|c} \text{Class} & \text{Frequency} \\ \hline 0 - 1 & 6 \\ 2 - 3 & 6 \\ 4 - 5 & 6 \\ 6 - 7 & 5 \\ 8 - 9 & 7 \\ \end{array} \]

By examining the frequencies, we can describe the shape of the histogram. The frequencies are relatively close to each other, with no significant skewness to the left or right. Therefore, the histogram is best described as symmetric.

Final Answer