Question

The ages of the first 16 U.S. presidents at the time of their first inauguration are displayed below:presidentageWashington57John Adams61Jefferson57Madison57Monroe58J.Q. Adams57Jackson61Van Buren54W.H. Harrison 68Tyler51Polk49Taylor64Fillmore50Pierce48Buchanan65Lincoln52Compute each of the following summary statistics. Round your answers to the nearest 0.1 years. Consider the data to be the full population.median = yearsIQR = yearsmean = yearsstandard deviation = years

Answer 1

Step 1

Write the numbers

57, 61, 57, 57, 58, 57, 61, 54, 68, 51, 49, 64, 50, 48, 65, and 52.

Step 2

Rearrange

48, 49, 50, 51, 52, 54, 57, 57. 57, 57, 58, 61, 61, 64, 65, 68,

`\begin{gathered} meadian\text{ is the middle number} \\ =\text{ 57} \\ \end{gathered}`
`\begin{gathered} IQR\text{ = Q3 - Q1} \\ \\ Q1\text{ = }(51+52)/(2)=51.5 \\ Q3\text{ = }\frac{61\text{ + 61}}{2}\text{ = 61} \\ \\ IQR\text{ = Q3 - Q1 = 61-51.5 = 9.5} \end{gathered}`

step

`mean\text{ = }(909)/(16)\text{ = 56.8}`

`\begin{gathered} \mathrm{The\:standard\:deviation,\:}\sigma \left(X\right)\mathrm{,\:is\:the\:square\:root\:of\:the\:variance:\quad } \\ \sigma \left(X\right)=\sqrt{\frac{\sum _(i=1)^n\left(x_i-\bar{x}\right)^2}{n-1}} \\ 5.9 \end{gathered}`

Standard deviation = 5.9