On September $29,2005,$ John Roberts was sworn in as the Chief Justice of the United States. Since $1869$ there have been nine justices at any one time on the Supreme Court of the United States: one chief justice and eight associate justices. $($Prior to that time, the number of justices varied from six to ten.$)$ From the court's inception in $1789$ to the present day, $17$ men have served as chief justice of the Supreme Court, including Justice Roberts. The previous $16$ chief justices are listed in the table below, along with the length of their tenure $($in days$).$ This data was retrieved from the Web site of the Supreme Court $($www$.$supremecourtus.gov$).$

chief justice tenure

John Jay $2079$

John Rutledge $125$

Oliver Ellsworth $1742$

John Marshall $12542$

Roger B$.$ Taney $10425$

Salmon P$.$ Chase $3065$

Morrison R$.$ Waite $5133$

Melville W$.$ Fuller $7938$

Edward D$.$ White $3804$

William Howard Taft $3129$

Charles E$.$ Hughes $4144$

Harlan F$.$ Stone $1754$

Frederick M$.$ Vinson $2633$

Earl Warren $5740$

Warren E$.$ Burger $6304$

William H$.$ Rehnquist $6917$

Compute each of the following summary statistics. Round your answers to the nearest day.

median $=$

$5436\mathrm{.}5$

Incorrect days

IQR $=$

$3852$

Incorrect days

mean $=$

$5300\mathrm{.}12$

Incorrect days

standard deviation