Question

# Find the actual lower and upper class limits and also the class marks of the classes :$$1.1 - 2.0, 2.1 - 3.0$$ and $$3.1 - 4.0.$$

A
Actual lower limits : 1.05,2.05,3.05
Actual upper limits : 2.05,3.05,4.05
Class marks : 1.55,2.55,3.55
B
Actual lower limits : 1.5,2.5,3.5
Actual upper limits : 2.5,3.5,4.5
Class marks : 2.5,3.5,4.5
C
Data insufficient
D
None of these

Solution

## The correct option is D Actual lower limits : $$1.05, 2.05, 3.05 \quad$$Actual upper limits : $$2.05, 3.05, 4.05 \quad$$Class marks : $$1.55, 2.55, 3.55$$$$d=\dfrac{LowerLimit-upperLimitOfPreviousColumn}{2}=\dfrac{2.1-2.0}{2}=0.05$$Class mark is the mid point of the class interval.Upper limit is highest value of the class interval and the actual upper limit is obtained by adding $$0.5$$ to the highest number if number is represented as whole number or add $$0.05$$ to the highest number if the number is represented as decimal.Similarly, the lower limit is the smallest value of the class interval and the actual lower limit is obtained by subtracting $$0.5$$ to the smallest number if the number is whole number or subtract $$0.05$$ to the smallest number if the number is decimal.Given, class intervals are $$1.1-2.0, 2.1-3.0,3.1-4.0$$Since, the intervals are represented in decimal, we add and subtract $$0.05$$ to get the actual limits.For class interval $$1.1-2.0$$,Class mark is $$\dfrac{1.1+2.0}{2}=\dfrac{3.1}{2}=1.55$$Actual upper limit is $$2.0+0.05=2.05$$ andactual lower limit is $$1.1-0.05=1.05$$Similarly for $$2.1-3.0$$,Class mark is $$\dfrac{2.1+3.0}{2}=2.55$$Actual upper limit is $$3.0+0.05=3.05$$ andactual lower limit is $$2.1-0.05=2.05$$Similarly for $$3.1-4.0$$,Class mark is $$\dfrac{3.1+4.0}{2}=3.55$$Actual upper limit is $$4.0+0.05=4.05$$ andactual lower limit is $$3.1-0.05=3.05$$Therefore, actual upper limits are $$2.05,3.05,4.05$$Actual lower limits are $$1.05,2.05,3.05$$Class marks are $$1.55,2.55,3.55$$Mathematics

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