Class Interval	Frequency ${f_i}$	Mid=point ${x_i}$	${y_i} = \frac{{{x_i} – 42.5}}{4}$	${f_i}^2$	${f_i}{y_i}$	${f_i}{y_i}^2$
$33-36$	$15$	$34.5$	$-2$	$4$	$-30$	$60$
$37-40$	$17$	$38.5$	$-1$	$1$	$-17$	$17$
$41-44$	$21$	$42.5$	$0$	$0$	$0$	$0$
$45-48$	$22$	$46.5$	$1$	$1$	$22$	$22$
$49-52$	$25$	$50.5$	$2$	$4$	$50$	$100$
	$100$				$25$	$199$

here, $N=100,$ $h=4$

Let the assumed mean, $A,$ be $42.5$

Mean,   $\bar x = A + \frac{{\sum\limits_{i = 1}^5 {{f_i}{y_i}} }}{N} \times h$

$ = 42.5 + \frac{{25}}{{100}} \times 4 = 43.5$

Variance,  $\left( {{\sigma ^2}} \right) = \frac{{{h^2}}}{{{N^2}}}\left[ {N\sum\limits_{i = 1}^5 {{f_i}{y_i}^2 – {{\left( {\sum\limits_{i = 1}^5 {{f_i}{y_i}} } \right)}^2}} } \right]$

$=\frac{16}{10000}\left[100 \times 199-(25)^{2}\right]$

$=\frac{16}{10000}[19900-625]$

$=\frac{16}{10000} \times 19275$

$=30.84$

$\therefore$ Standard deviation $(\sigma)=5.55$