Question

here is a data set:
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 and the first lower class limit should be.
what is the best class width for this data set?
optimal class width =
what should be the first lower class limit?
1st lower class limit =
question help: video

Explanation:

Step1: Find the maximum and minimum values

First, find the maximum value $x_{max}$ and minimum value $x_{min}$ in the data - set. By looking at the data, $x_{max}=470$ and $x_{min}=227$.

Step2: Calculate the range

The range $R$ is given by $R = x_{max}-x_{min}$. So, $R=470 - 227=243$.

Step3: Determine the class width

We want 10 classes. The class width $w$ is calculated as $w=\frac{R}{k}$, where $k = 10$ (the number of classes). $w=\frac{243}{10}=24.3$. Since we want a "nice" class width (a whole - number for simplicity), we round up to the next whole number. So, $w = 25$.

Step4: Determine the first lower - class limit

The first lower - class limit should be a multiple of the class width and less than or equal to the minimum value. The closest multiple of 25 that is less than or equal to 227 is 225.

Answer:

optimal class width = 25
1st lower class limit = 225