Question

How to find \[{x_i}\] in statistics?

Answer 1

Hint: In this given question, we have to tell how to find \[{x_i}\] in statistics. We will use the fact that the class mark (\[{x_i}\]) is the average of the range of the class interval. Hence we will use the formula \[{x_i} = \dfrac{{{x_l} + {x_u}}}{2}\] .where \[{x_l}\] is the upper and \[{x_u}\] is the lower limit of the class interval.

Complete step-by-step answer:
The given question is based on statistics. Statistics is the branch of mathematics which deals with collection, organisation, interpretation and analysis of numbers or data.
Data is the information which is collected, organized, interpreted and analysed. Data can be in two forms – grouped or ungrouped.
Ungrouped data are just numbers. While grouped data lies between some intervals.
We can find the mean median and mode of any data.
Class interval is a range in which the values lie. It has an upper and lower limit. For example: \[\left( {40 - 50} \right)\] is a class interval of size 10 whose upper limit is \[50\] and lower limit is \[40\] .
Class mark denoted by is the average of the upper limit and lower limit of the class interval.
Step to find class marks:
Find the upper limit and lower limit of class interval.
Add the lower and upper limit of class interval.
Divide the resultant sum by \[2\].
We will get the class mark.
We can also use the formula to find the class mark as follow: \[{x_i} = \dfrac{{{x_l} + {x_u}}}{2}\]
For example, consider the class interval \[\left( {40 - 50} \right)\]. Here the lower limit is \[40\] and upper limit is \[50\].
Hence, the class mark is given by \[{x_i} = \dfrac{{40 + 50}}{2} = \dfrac{{90}}{2} = 45\].

Note: In this problem, similarly we can find the class mark in statistics.
Class interval is the range of intervals into which the values lie.
Class size is the difference between upper limit and lower limit.
Class mark is used to find the mean, median and mode of any data.
\[Mean = \dfrac{{\sum {{x_i}{f_i}} }}{{\sum {{f_i}} }}\] where \[{x_i}\] is the class mark and \[{f_i}\] is the frequency (number of time data appear in a particular interval. ).