Question

In the following grouped frequency distribution table class marks are given.

Class Marks	$10$	$22$	$34$	$46$	$58$	$70$
Frequency	$6$	$14$	$20$	$21$	$9$	$5$

(i) Construct class intervals of the data. (Exclusive class intervals)
(ii) Construct less than cumulative frequencies and
(iii) Construct greater than cumulative frequencies

Answer 1

$\Rightarrow$ Class size $=22-10=12$

$\therefore$ $\frac{12}{2}=6$

Now, we are going to subtract and add $6$ in class marks.

$\therefore$ Class intervals are

$6-16,16-28,28-40,40-52,52-64,64-76.$

$\Rightarrow$ Construct less than cumulative frequency table:

$Class-Interval$	$L.C.F$
Less than $16$	$6$
Less than $28$	$6+14=20$
Less than $40$	$20+20=40$
Less than $52$	$40+21=61$
Less than $64$	$61+9=70$
Less than $76$	$70+5=75$

$\Rightarrow$ Construct greater than cumulative frequency table:

$Class-Interval$	$G.C.F$
Greater than $6$	$6+69=75$
Greater than $16$	$14+55=69$
Greater than $28$	$20+35=55$
Greater than $40$	$21+14=35$
Greater than $52$	$9+5=14$
Greater than $64$	$5$