You previously created a five-number summary of the lengths of $23$ newborns at the Dallas University Health Center. The measurements, in centimeters, were:

$46.4,46.9,47.7,48.1,48.5,48.5,48.8,49.0,49.3,50.0,50.1,50.4,50.6,51.1,51.4,51.8,52.4,52.5,53.2,53.8,54.4,55.1,55.9$ checksum 1165.9

Determine if it is appropriate to summarize the data using the mean and standard deviation. If it is appropriate, justify your reasoning and calculate the mean and standard deviation. If it is not appropriate, explain why not, and calculate the median and IQR. Consider the precision of the measurements when giving the result.