Question

Convert the given frequency distribution into a continuous grouped frequency distribution. In which intervals would $153.5$ and $157.5$ be included?

Class interval	Frequency
$150-153$	$7$
$154-157$	$7$
$158-161$	$15$
$162-165$	$10$
$166-169$	$5$
$170-173$	$6$

Answer 1

Let us consider the classes $150-153$ and $154-157$

The lower limit of $154-157$$=154$

The upper limit of $150-153$$=153$

The difference of width between classes$=154-153=1$

Half of the difference of the width $=\frac{1}{2}=0.5$

The new class interval formed can be obtained by adding the half of difference to upper limit and subtracting half of the difference to lower limit.

Therefore, The new class interval formed from $150-153$$=(150-0.5)-(153+0.5)=149.5-153.5$

Now, the continuous classes formed for all class interval can be represented in a table as:

Class Interval	Frequency
$149.5-153.5$	$7$
$153.5-157.5$	$7$
$157.5-161.5$	$15$
$161.5-165.5$	$10$
$165.5-169.5$	$5$
$169.5-173.5$	$6$

From the table, it can be observe that $153.5$ belongs to the class interval $153.5-157.5$and $157.5$ belongs to the class interval $157.5-161.5$.

Hence, $153.5$ belongs to the class interval $153.5-157.5$and $157.5$ belongs to the class interval $157.5-161.5$