Solution
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,
[tex]\begin{gathered} meadian\text{ is the middle number} \\ =\text{ 57} \\ \end{gathered}[/tex][tex]\begin{gathered} IQR\text{ = Q3 - Q1} \\ \\ Q1\text{ = }\frac{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}[/tex]step
[tex]mean\text{ = }\frac{909}{16}\text{ = 56.8}[/tex][tex]\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}[/tex]Standard deviation = 5.9
