The data is obtained in tabular form as follows.

${x_i}$ $60$ $61$ $62$ $63$ $64$ $65$ $66$ $67$ $68$
${f_i}$ $2$ $1$ $12$ $29$ $25$ $12$ $10$ $4$ $5$

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The data is obtained in tabular form as follows.

${x_i}$ ${f_i}$ ${f_i} = \frac{{{x_i} - 64}}{1}$ ${y_i}^2$ ${f_i}{y_i}$ ${f_i}{y_i}^2$
$60$ $2$ $-4$ $16$ $-8$ $32$
$61$ $1$ $-3$ $9$ $-3$ $9$
$62$ $12$ $-2$ $4$ $-24$ $48$
$63$ $29$ $-1$ $1$ $-29$ $29$
$64$ $25$ $0$ $0$ $0$ $0$
$65$ $12$ $1$ $1$ $12$ $12$
$66$ $10$ $2$ $4$ $20$ $40$
$67$ $4$ $3$ $9$ $12$ $36$
$68$ $5$ $4$ $16$ $20$ $80$
  $100$ $220$   $0$ $286$

Mean, $\bar x = A\frac{{\sum\limits_{i = 1}^9 {{f_i}{y_i}} }}{N} \times h = 64 + \frac{0}{{100}} \times 1 = 64 + 0 = 64$

Variance,   ${\sigma ^2} = \frac{{{h^2}}}{{{N^2}}}\left[ {N\sum\limits_{i = 1}^9 {{f_i}{y_i}^2 - \left( {\sum\limits_{i = 1}^9 {{f_i}{y_i}^2} } \right)} } \right]$

$=\frac{1}{100^{2}}[100 \times 286-0]$

$=2.86$

$\therefore$ Standard deviation $(\sigma)=\sqrt{2.86}=1.69$

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