Question

A set of data contains 57 observations. The lowest value is 41 and the largest is 148. The data are to be organized into a frequency distribution.

a. How many classes would you suggest?



b. What would you suggest as the lower limit of the first class?

Answer 1

a. If $k$ is the number of classes and $n$ is the number of observations, then for class intervals, select the smallest $k$ such that $2^k>n.$

Given that $n=57$

$$2^5<57<2^6$$

We can take 6 classes.

b. If $U$ is the highest observed value and $L$ is the lowest observed value, and $w$ is the class width (class interval), then we can select $w$ such that

$$w\geq{U-L \over k}$$

Given that $U=148, L=41, k=6.$ Class limits have the same accuracy as the data values.

Then

$$w\geq{148-41 \over 6}$$ $$w\geq18$$

Use the minimum data entry $L=41$ as the lower limit of the first class

$$\begin{matrix} Class\ limits & Class\ boundaries \\ 41-58 & 40.5-58.5 \\ 59-76 & 58.5-76.5 \\ 77-94 & 76.5-95.5 \\ 95-112 & 94.5-112.5\\ 113-130 & 112.5-130.5 \\ 131-148 & 130.5-148.5 \end{matrix}$$