the class-marks of classes in distribution are 6,10,14,18,22,26,30.find
(a)class size
(b)lower limit of second class
(c)upper limit of last class
(d)third class
Explain in detail.
(a) Class size refers to the difference between the upper limit and the lower limit of a class interval. To find the class size, we need to calculate the difference between any two consecutive class marks.
Let's take the differences between consecutive class marks:
10 - 6 = 4
14 - 10 = 4
18 - 14 = 4
22 - 18 = 4
26 - 22 = 4
30 - 26 = 4
As we can see, the differences between all consecutive class marks are consistent at 4. Therefore, the class size is 4.
(b) The lower limit of the second class is the lower boundary of the second class interval. To find this, we need to identify the class mark that falls at the beginning of the second class interval.
In this case, the class marks are 6, 10, 14, 18, 22, 26, 30.
The second class interval starts at 10. Therefore, the lower limit of the second class is 10.
(c) The upper limit of the last class is the upper boundary of the last class interval. To find this, we need to identify the class mark that falls at the end of the last class interval.
In this case, the class marks are 6, 10, 14, 18, 22, 26, 30.
The last class interval ends at 30. Therefore, the upper limit of the last class is 30.
(d) To determine the third class, we need to count the classes one by one and identify the class that corresponds to the given position.
In this case, the class marks are 6, 10, 14, 18, 22, 26, 30.
Counting from left to right, the third class is the one that starts with the class mark 14 and ends with the class mark 18.
Therefore, the third class is the interval (14 - 18).
To find the answers to the given questions, we need to understand the concept of class intervals and class size.
(a) Class size:
The class size refers to the difference between the upper limit and lower limit of a class interval.
In this case, the class marks are given as 6, 10, 14, 18, 22, 26, and 30.
The class size can be found by taking the difference between any two consecutive class marks. Let's take the difference between 10 and 6.
Class size = 10 - 6 = 4
So, the class size is 4.
(b) Lower limit of the second class:
To find the lower limit of a class, we need to subtract half of the class size from the class mark.
In this case, the class mark of the second class is 10.
So, let's find the lower limit by subtracting half of the class size (4/2) from 10.
Lower limit of the second class = 10 - (4/2) = 10 - 2 = 8
Therefore, the lower limit of the second class is 8.
(c) Upper limit of the last class:
To find the upper limit of the last class, we need to add half of the class size to the class mark.
In this case, the class mark of the last class is 30.
So, let's find the upper limit by adding half of the class size (4/2) to 30.
Upper limit of the last class = 30 + (4/2) = 30 + 2 = 32
Therefore, the upper limit of the last class is 32.
(d) Third class:
To find the third class, we need to count the class marks from the beginning.
In this case, the class marks are 6, 10, 14, 18, 22, 26, 30.
The third class is the class with the third class mark.
So, the third class is 14.
To summarize:
(a) Class size: 4
(b) Lower limit of second class: 8
(c) Upper limit of last class: 32
(d) Third class: 14