Question

step 1
first, find the class width for a frequency table with 7 classes.
recall that a frequency table partitions data into classes or intervals of equal width. the class width is computed by dividing the difference of the largest data value and the smallest data value by the desired number of classes.
class width = \\(\frac{\text{largest data value} - \text{smallest data value}}{\text{desired number of classes}}\\)
we are given that the data set has a low value of 30 and a high value of 137. additionally, we want a frequency table with seven classes. substitute these values into the formula for class width and, for now, round the result to two decimal places.
class width = \\(\frac{\text{largest data value} - \text{smallest data value}}{\text{desired number of classes}}\\)
= \\(\frac{137 - \square}{7}\\)
= \\(\frac{\square}{7}\\)
= \square

Explanation:

Step1: Identify smallest data value

The smallest data value is 30. So we substitute 30 into the formula.
$\frac{137 - 30}{7}$

Step2: Calculate numerator

Calculate \(137 - 30 = 107\).
$\frac{107}{7}$

Step3: Divide to find class width

Divide 107 by 7: \(107\div7\approx15.29\) (rounded to two decimal places).

Answer:

First blank: 30; Second blank: 107; Third blank: 15.29