a) Mean $ = 45 - 148/36 = 40.9$ or $1472/36$

EITHER

$Var = 3089/36 - {\left( { - 148/36} \right)^2} = 68.9$

$sd = 8.30$

OR

$\sum {{x^2}}  = 3089 - 36 \times {45^2} + 90 \times 1472 = 62669$

$Var = \left( {\frac{{62669}}{{36}} - {{\left( {\frac{{1472}}{{36}}} \right)}^2}} \right)$

$sd = 8.30$

b) New $\sum {\left( {x - 45} \right)}  =  - 148 - 16 =  - 164$

New $\sum {{{\left( {x - 45} \right)}^2}}  = 3089 + {16^2} = 3345$

New $sd = \sqrt {3345/37 - {{\left( { - 164/37} \right)}^2}} $

$ = 8.41$

OR

OR $\sum x  = 36 \times 45 - 148 = 1472$

New $\sum x  = 1472 + 29 = 1501$

$\sum {{x^2}}  = 3089 - 36 \times {45^2} + 90 \times 1472 = 62669$

New $\sum {{x^2}}  = 62669 + {29^2}\left( { = 63510} \right)$

New $sd = \sqrt {63510/37 - {{\left( {1501/37} \right)}^2}} $

$ = 8.41$