Observe the given frequency table to answer the following: Class … - Vidyadip

Question

Observe the given frequency table to answer the following:

Class Interval	$20 - 24$	$25 29$	$30 - 34$	$35 - 39$	$40 - 44$	$45 - 49$
Frequency	$6$	$12$	$10$	$15$	$9$	$2$

$a$. The true class limits of the fifth class.;$b$. The size of the second class.;$c$. The class boundaries of the fourth class.$d$. The upper and lower limits of the sixth class.$e$. The class mark of the third class.

✓

Answer

$a$. Fifth class : $40-44$
Since classes are inclusive, we have
Adjustment factor
$ =\frac{25-24}{2}$
$=\frac{1}{2}$
$=0.5 $
$\therefore$ True lower limit of $5^{\text {th }}$ class $=40-0.5=39.5$
True Upper limit of $5^{\text {th }}$ class $=44+0.5=44.5$.
$b$. Size of class $25-29=29.5-24.5=5$.
$c$. True lower limit of $4^{\text {th }}$ class $=35-0.5=34.5$True Upper limit of $4^{\text {th }}$ class $=39+0.5=39.5$
$\therefore$ Class boundaries of $4^{th}$ class are $34.5$ and $39.5 .$
$d$. Lower limit of $6^{\text {th }}$ class $=45-0.5=44.5$
Upper limit of $6^{\text {th }}$ class $=49+0.5=49.5$.
$e$. True lower limit of $3^{\text {rd }}$ class $=30-0.5=29.5$
True Upper limit of $3^{\text {rd }}$ class $=34+0.5=34.5$
$ \therefore$ Class mark
$=\frac{29.5+34.5}{2}$
$=32 . $

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