Part $1.$ An angle is observed repeatedly using the same equipment and procedures. The following values are measured:

$23{30}^{\text{'}}{37}^{\text{'}\text{'}}$

$23{29}^{\text{'}}{47}^{\text{'}\text{'}}$

$23{30}^{\text{'}}{30}^{\text{'}\text{'}}$

$23{29}^{\text{'}}{53}^{\text{'}\text{'}}$

Calculate the angle's most probable value $($in decimal form, with correct # of significant digits$)$

Part $2.$ Calculate the standard deviation of the measurements above