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, 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: 1.5, 2.5, 3.5
C) Data insufficient
D) None of these

Answer 1

Hint: Class mark is the mid point of the class interval. Upper limit is the highest value of the class interval.
Similarly, the lower limit is the smallest value of the class interval. For finding the actual upper limits and actual lower limits , we need to make the upper limit of a certain class and lower limit of the next class to be equal and same for the lower limit.
     $$d={\displaystyle \frac{\left(\text{upper limit - lower limit}\right)}{2}}={\displaystyle \frac{2.1-2.0}{2}}=0.05$$
     $$$$ Upper limit is the highest value of the class interval and the actual upper limit is obtained by adding 0.5 to the highest number if the number is represented as a 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 the whole number or subtract 0.05 to the smallest number if the number is decimal.

Complete step by step answer:
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 $${\displaystyle \frac{(1.1+2.0)}{2}}={\displaystyle \frac{3.1}{2}}=1.55$$
 Actual upper limit is 2.0+0.05=2.05 and
actual lower limit is 1.1−0.05=1.05
 Similarly for 2.1−3.0,
 Class mark is $${\displaystyle \frac{(2.1+3.0)}{2}}={\displaystyle \frac{5.1}{2}}=2.55$$
 Actual upper limit is 3.0+0.05 = 3.05 and
actual lower limit is 2.1−0.05 = 2.05
 Similarly for 3.1−4.0,
 Class mark is $${\displaystyle \frac{(3.1+4.0)}{2}}={\displaystyle \frac{7.1}{2}}=3.55$$

Actual upper limit is 4.0+0.05=4.05 and
actual 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

Therefore the correct option is A.

Note:
Learn the differences between upper limit , lower limit, actual upper limit and actual lower limit. We should add 0.5 when it is a=whole number and 0.05 when it is a decimal for both lower limit and upper limit. Class mark is the midpoint of the class interval.