Question

The class mark of a class interval is
1.\[Lower{\text{ }}limit{\text{ }} + {\text{ }}Upper{\text{ }}limit\]
2.\[Upper{\text{ }}limit{\text{ - Lower }}limit\]
3.\[\dfrac{1}{2}\left( {Lower{\text{ }}limit{\text{ }} + {\text{ }}Upper{\text{ }}limit} \right)\]
4.\[\dfrac{1}{4}\left( {Lower{\text{ }}limit{\text{ }} + {\text{ }}Upper{\text{ }}limit} \right)\]

Answer 1

Hint: Class mark of an interval is also known as the middle value of that interval. It represents the middle value of an interval. To find a class mark, all we need to do is take the average of the upper and lower limit of the interval.

Complete step-by-step answer:
Class mark is generally considered as the overall representation of the interval, because it occupies the middle position of a particular interval. It is used to find the mean by step deviation method.
To find the class mark of an interval, all we need to do is take the average of the upper and lower limit, which will give us the mid value or the class mark.
Thus, if the lower limit of an interval is \[l\] and upper limit is \[u\], then the interval be \[l - u\], and its class mark will \[\dfrac{{l + u}}{2}\] that is \[\dfrac{1}{2}\left( {Lower{\text{ }}limit{\text{ }} + {\text{ }}Upper{\text{ }}limit} \right)\].
Hence, option (C) will be the correct option.

Note: Class mark in a bar graph is the middle bar. If the data is distributed symmetrically, then the class mark will accurately represent the average of that interval. However that may not always be the case. For such cases where the data is unevenly distributed, we have to find the mean of interval by some other method, because class marks will be the average of only the extreme values and it doesn’t consider the values lying in-between. The middle value which has a high frequency can easily affect the actual average of the interval but won’t have any effect on the class mark.