Question

In a frequency distribution, the mid-value of a class is $10$ and the width of the class is $6$. The lower limit of the class is:
A) $6$
B) $7$
C) $8$
D) ​​​​​​​$12$

Answer 1

The answer is B.

Let $x$ and $y$ be the upper and lower class limit in a frequency distribution.

Now, mid value of a class $=\frac{x+y}{2}=10$ [given]

$\Rightarrow x+y=20\dots \dots \left(i\right)$
Also, given that, width of class $=6$

$\Rightarrow x-y=6\dots \dots \left(ii\right)$
On adding equations $\left(i\right)$ and $\left(ii\right)$, we get, $2x=20+6$
$\Rightarrow 2x=26\Rightarrow x=13$
On putting $x=13$ in $\left(i\right)$, we get,
$13+y=20\Rightarrow y=7$
Hence, the lower limit of the class is $7$.