Question

the monthly salaries of a sample of 100 employees ranged from a low of $1,040 to a high of $1,720. if we want to condense the data into seven classes, what are the class limits for the third class?

Answer 1

To determine the third class limits for salary data when forming seven classes, calculate the class width by dividing the range of salaries ($680) by the number of classes (7), and round to the nearest whole number. With the class width of $98, the third class limits are $1,333 to $1,332.

Step-by-step explanation:

To find the class limits for the third class when the monthly salaries of a sample of 100 employees range from a low of $1,040 to a high of $1,720 and you want to condense the data into seven classes, you first need to calculate the class width.

First, find the range of the data:

Range = Highest salary - Lowest salary

Range = $1,720 - $1,040

Range = $680

Next, divide the range by the number of classes:

Class width = Range / Number of classes

Class width = $680 / 7

Class width = approximately $97.14

Since you can't have a fraction of a dollar in salary, you would round this up to the nearest whole number, making the class width $98. This ensures that all values fit into the seven classes without overlap or gaps.

Now, calculate the actual limits for the third class. First class starts at the lowest salary, so:

First class limits: $1,040 to $1,040 + $98 - 1 = $1,137

Second class limits: $1,137 + 1 to $1,137 + $98 = $1,235

Third class limits: $1,235 + 1 to $1,235 + $98 = $1,333 to $1,332