Question

here is a data set: 22.9 48 43.7 35.5 15.3 8.8 22.1 25.8 9 38.2 20.8 21.7 12.8 25.6 36.5 4.9 28.6 45.2 13.3 34.4 42.5 23.2 31 21.9 15.9 28.5 32.5 31.5 the goal is to construct a grouped frequency distribution table (gfdt) for this data set. the gfdt should have 10 classes with a
ice\ class width. each class should contain its lower class limit, and the lower class limits should all be multiples of the class width. this problem is to determine what the class width should be. what is the range of this data set? range = using this value, if the goal is to have 10 classes, what is the nicest class width? optimal class width = question help: video

Explanation:

Step1: Find the maximum and minimum values

The maximum value in the data - set is $48$ and the minimum value is $4.9$.

Step2: Calculate the range

The range is calculated as $R=\text{Max}-\text{Min}$. So, $R = 48 - 4.9=43.1$.

Step3: Calculate the class width

The number of classes $n = 10$. The class width $w=\frac{R}{n}=\frac{43.1}{10}=4.31$. Since we want a "nice" class width (a whole - number or a simple fraction), we round up to $5$.

Answer:

range = $43.1$
optimal class width = $5$