Questions: Wachesaw Manufacturing Incorporated produced the following number of units in the last 16 days. 27, 27, 27, 28, 27, 25, 25, 28, 26, 28, 26, 28, 31, 30, 26, 26 The information is to be organized into a frequency distribution. Click here for the Excel Data File Required: a. How many classes would you recommend? Number of classes b. What class interval would you suggest? Note: Round your answer to 1 decimal place. Class interval

Solution Steps

To solve the given problem, we need to determine the number of classes and the class interval for a frequency distribution of the data provided.

1. Determine the number of classes: Use Sturges' formula, which is \( k = 1 + 3.322 \log_{10}(n) \), where \( n \) is the number of data points.
2. Calculate the class interval:
   • Find the range of the data by subtracting the minimum value from the maximum value.
   • Divide the range by the number of classes to get the class interval.

To determine the number of classes, we use Sturges' formula: \[ k = 1 + 3.322 \log_{10}(n) \] Given \( n = 16 \): \[ k = 1 + 3.322 \log_{10}(16) \] \[ k \approx 1 + 3.322 \times 1.2041 \] \[ k \approx 1 + 4.0000 \] \[ k \approx 5.0000 \] Rounding up to the nearest whole number: \[ k = 6 \]

The range of the data is calculated as: \[ \text{Range} = \max(\text{data}) - \min(\text{data}) \] Given the data: \[ \text{Range} = 31 - 25 \] \[ \text{Range} = 6 \]

The class interval is calculated by dividing the range by the number of classes: \[ \text{Class Interval} = \frac{\text{Range}}{k} \] \[ \text{Class Interval} = \frac{6}{6} \] \[ \text{Class Interval} = 1.0000 \]

Final Answer