The monthly salaries of a sample of 100 employees were rounded to the nearest ten dollars. They ranged from a low of $1,040 to a high of $1,720. If we want to condense the data into seven classes, what is the most convenient class interval?
A. $50
B. $100
C. $150
D. $200
E. none of the above
The difference between the low and the high is $680. If we want to divide that difference into seven classes, $680/7 is close to $100. An interval of $100 would make the most sense here.
50
To find the most convenient class interval, we need to calculate the range of the data and divide it by the desired number of classes.
The range is the difference between the highest and lowest values:
Range = Highest Value - Lowest Value
Range = $1,720 - $1,040
Range = $680
Now, we divide the range by the desired number of classes (7):
Class Interval = Range / Number of Classes
Class Interval = $680 / 7
Class Interval ≈ $97.14
Since we want to round to the nearest value, the most convenient class interval would be $100.
Therefore, the answer is B. $100.
To determine the most convenient class interval, we need to consider the range of the data and the number of classes we want to create.
The range of the data is the difference between the highest and lowest values: $1,720 - $1,040 = $680.
To find the most convenient class interval, we divide the range by the number of classes we want to create. In this case, we want to create seven classes.
$680 / 7 ≈ $97.14
We round this number to the nearest whole number to get the class interval.
Therefore, the most convenient class interval in this case is $100, which is option B.