Questions: The number of hospital beds in a sample of 20 hospitals is shown below. Construct a frequency distribution and a frequency histogram for the data set using 5 classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, positively skewed, or none of these. 167 180 128 132 176 156 165 224 149 135 193 205 149 255 258 242 288 134 200 177 Construct a frequency distribution for the data set using 5 classes. (Type whole numbers.) Class Frequency 128-160 161-193 194-226 227-259 260-292 Construct a frequency histogram for the data set using the frequency distribution. Choose the correct answer below.

Solution Steps

First, we need to organize the data into a frequency distribution with 5 classes. The data set is:

\[ 167, 180, 128, 132, 176, 156, 165, 224, 149, 135, 193, 205, 149, 255, 258, 242, 288, 134, 200, 177 \]

To determine the class width, we first find the range of the data:

• Minimum value: 128
• Maximum value: 288

Range = \( 288 - 128 = 160 \)

Class width = \(\frac{\text{Range}}{\text{Number of classes}} = \frac{160}{5} = 32\)

Using the class width of 32, we construct the frequency distribution:

• Class 1: 128-160
• Class 2: 161-193
• Class 3: 194-226
• Class 4: 227-259
• Class 5: 260-292

Now, count the number of data points in each class:

• 128-160: 6 (128, 132, 135, 134, 149, 156)
• 161-193: 6 (167, 180, 176, 165, 193, 177)
• 194-226: 2 (205, 200)
• 227-259: 3 (255, 258, 242)
• 260-292: 3 (288)

The frequency histogram is a graphical representation of the frequency distribution. Each class interval is represented on the x-axis, and the frequency of each class is represented on the y-axis.

Based on the frequency distribution, the histogram will have the following frequencies:

• 128-160: 6
• 161-193: 6
• 194-226: 2
• 227-259: 3
• 260-292: 3

The histogram is likely to be positively skewed because the frequencies decrease as the class intervals increase.

Final Answer