Finite Math Examples

Find the Upper and Lower Class Boundaries of the Frequency Table
ClassFrequency19.55-21.82321.83-24.1524.11-26.38926.39-28.66628.67-30.942
Step 1
The lower limit for every class is the smallest value in that class. On the other hand, the upper limit for every class is the greatest value in that class.
ClassFrequency(f)LowerLimitsUpperLimits19.55-21.82319.5521.8221.83-24.1521.8324.124.11-26.38924.1126.3826.39-28.66626.3928.6628.67-30.94228.6730.94
Step 2
Class boundaries are the numbers used to separate classes. The size of the gap between classes is the difference between the upper class limit of one class and the lower class limit of the next class. In this case, gap=21.83-21.82=0.01.
gap=0.01
Step 3
The lower boundary of each class is calculated by subtracting half of the gap value 0.012=0.005 from the class lower limit. On the other hand, the upper boundary of each class is calculated by adding half of the gap value 0.012=0.005 to the class upper limit.
ClassFrequency(f)LowerLimitsLowerBoundariesUpperLimitsUpperBoundaries19.55-21.82319.5519.55-0.00521.8221.82+0.00521.83-24.1521.8321.83-0.00524.124.1+0.00524.11-26.38924.1124.11-0.00526.3826.38+0.00526.39-28.66626.3926.39-0.00528.6628.66+0.00528.67-30.94228.6728.67-0.00530.9430.94+0.005
Step 4
Simplify the lower and upper boundaries columns.
ClassFrequency(f)LowerLimitsLowerBoundariesUpperLimitsUpperBoundaries19.55-21.82319.5519.54521.8221.82521.83-24.1521.8321.82524.124.10524.11-26.38924.1124.10526.3826.384926.39-28.66626.3926.38528.6628.66528.67-30.94228.6728.66530.9430.945
Step 5
Add the lower and upper class boundaries columns to the original table.
ClassFrequency(f)LowerBoundariesUpperBoundaries19.55-21.82319.54521.82521.83-24.1521.82524.10524.11-26.38924.10526.384926.39-28.66626.38528.66528.67-30.94228.66530.945
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