Question

Write the formula to find the class-mark of a class interval?

Answer 1

Hint: In this given question, we have to write the formula to find the class mark of a class interval. We will use the fact that the class mark (denoted as \[{x_i}\]) is the average of the range of the class interval. Hence, we can give the formula using the formula to find the average of two numbers.
i.e., \[x = \dfrac{{a + b}}{2}\] where \[x\] is the average of the two numbers \[a\] and \[b\]

Complete step by step solution:
The given question based on class marks is a term of statistics in mathematics. In statistics, we deal with data or information in numeral form. We represent this data/information in the form of tables, graphs, and some meaningful order such as ascending or descending order to interpret and to draw some conclusion.
We can have data in ungrouped form or grouped form. In ungrouped form, the class mark is the number itself.
While grouped data lies between some intervals. The values of group data lie in between some interval (say upper limit and lower limit) which is called class interval.
Class interval is a range in which the values lie. It has an upper and lower limit. For example: \[\left( {40 - 60} \right)\] is a class interval whose upper limit is \[60\] and lower limit is \[40\]
Class mark denoted by \[{x_i}\] is the average/half of the upper limit and lower limit of the class interval.
To find the class mark of any class interval we proceed as follow:
First, we find the upper limit and lower limit of the given class interval.
We then add the upper limit and the lower limit of class interval.
Then we divide the resultant sum by \[2\].
Hence, we get the class mark.
We can also use the formula to find the class mark as follow: \[{x_i} = \dfrac{{{x_l} + {x_u}}}{2}\] where \[{x_u}\] and \[{x_l}\] is the upper and lower limit of the class interval respectively.
For example, consider the class interval \[\left( {40 - 60} \right)\]. Here the lower limit is \[40\] and upper limit is \[60\].
Hence, the class mark is given by \[{x_i} = \dfrac{{40 + 60}}{2} = \dfrac{{100}}{2} = 50\].
Similarly, we can find the class mark of any interval.

Note: In statistics, class mark is used to average the value of class interval.
We can use class marks to find the central tendency of data i.e., mean median, mode of grouped data.
Average is defined as the sum of observations divided by the number of observations. i.e., \[average = \dfrac{{sum \; of \; observation}}{{number \;of \; observation}}\].