Question

# Explain the meaning of the following terms:(i) Variable (ii) Class interval (iii) Class – size (iv) Class – mark (v) Frequency (vi) Class – limits (vii) True class limits

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Hint: All these terms are usually used in statistics.Statistics is the study of the collection analysis, interpretation, presentation and organization of data

Complete step by step solution:
(i) Variable: Any character that can vary from one individual to another.
(ii) Class interval: In the data of each group into which the raw data is considered is called as class – interval.
(iii) Class – size: The difference between the upper limit and lower limit of a class.
(iv)Class – mark: The middle value of the selected class size.
It can be calculated as: Class mark: $\dfrac{{Upper\,limit + lower\,limit}}{2}$
(v) Frequency: Number of values that fall in the range specified in that class i.e. the number of observations corresponding to the class.
(vi)Class – limits: Each class is bounded by two quantities, called class limits. The quantities on the left side are called lower limit while on the right side are called upper limit.
Example: $10{\text{ }}-{\text{ }}20$
Here: $10 -$lower limit
$20 -$upper limit
(vii) True class limits: In the inclusive form of frequency distribution, the true lower limit of a class is obtained by getting the upper limit of preceding class and lower limit of current class.
Example: $4 - 8,\,\,9\, - 13,\,\,14 - 18$and so on, means $9 - 8 = \dfrac{1}{2} = 0.5$then,
True lower limit of class $=$lower limit of class $- 0.5$
And true lower limit of class $=$ upper limit of class $+ 0.5$
In this case, true limit of the class is $4 - 8$ or $3.5 - 8.5$
In the exclusive form, the upper and lower limits of a class are respectively known as true upper limit and true lower limit
Example: $10 - 20,\,\,20 - 30,\,\,30 - 40$and so on, then class limits and true class limits are the same.

Note: Do not get confused with the quantities Class interval and class size. Even though both the quantities may sound similar, both are different quantities.