Question

Find the missing class interval for the following table given.

Length (mm)	Frequency
12-24	14
24-36	21
36-48	13
48-60	12
60-72	10
?	15
84-86	20
96-108	4
108-120	25

$\left( a \right){\text{ 72 - 84}}$
$\left( b \right){\text{ 70 - 80}}$
$\left( c \right){\text{ 76 - 82}}$
$\left( d \right){\text{ 71 - 81}}$

Answer 1

Hint: Here, in this question, we have to find the class interval on the allocated position. So for this, we will first see the common differences between the class intervals. And then by using the concept of reasoning or we can say number series we will easily find it out.

Complete step-by-step answer:
So we have two data given in the table one is the frequency and the other one is the length. We have to find out the class interval.
Since, if we see the length table, we can see that the difference between the class interval widths will be equal to
$ \Rightarrow 72 - 60$
And on solving it we get
$ \Rightarrow 12$
Similarly for the other pair, if we check it, we will get the same differences.
So the number at that position should also have to be the difference of $12$ .
So now for easy solving, we can check it with the options given to us.
Therefore, on checking we get that the interval $72 - 84$ will be the missing interval.
Hence, the option $\left( a \right)$ is correct.

Note: To understand the class interval in a line we can say that it is the range of each group of data. So by definition, we can say that it is the width of any class in a particular distribution. So if we have to define it mathematically, we can say it as the difference between the upper caste limit and lower case limit. So these are important lines everyone should know before solving such questions.