Q. 2.113 - Elementary Statistics

Question

Weights of 18- to 24-Year-Old Males. Refer to the weight data in Table $2.8$ on page 54 . Note that there are 37 observations, the smallest and largest of which are $129.2$ and$278.8$, respectively. Apply the preceding procedure to choose classes for cut point grouping. Use approximately eight classes. Note: If in Step 2 you decide on 20 for the class width and in Step 3 you choose 120 for the lower cut point of the first class, then you will get the same classes as used in Example 2.14; otherwise, you will get different classes (which is fine).

Step-by-Step Solution

Answer

The frequency of each class is shown in figure.

$\begin{array}{cc}\text{ Class limits }& \text{ Frequency }\\ 129-<148& 6\\ 178-<167& 10\\ 167-<186& 13\\ 186-<205& 4\\ 205-<224& 3\\ 224-<243& 0\\ 243-<262& 0\\ 262-<281& 1\end{array}$

Step 1: Given Information

Given in the question that, the weights of $18$ to $24$ year old males. There are total  observations.

Step 2: Explanation

According to the information, There are $8$ classes in all.

The width of the class is:

$\frac{278.8-129.2}{8}=\frac{149.6}{8}$

                           $=18.7$

                           $=19$.

Choose a lower class limit, such as $129$.

The cut points are the lower class limit, which has been extended by a $19$-class width.

Cut points $=129,148,167,186,205,224,243,262,281$.