Step 1
Given;
[tex]10,\:15,\:19,\:52,\:34,\:44,\:47,\:20,\:60,\:25[/tex]Step 2
Find the mean
[tex]\begin{gathered} The\:arithemtic\:mean\:\left(average\right)\:is\:the\:sum\:of\:the\:values\:in\:the\:set\: \\ \begin{equation*} divided\:by\:the\:number\:of\:elements\:in\:that\:set. \end{equation*} \\ \mathrm{If\:our\:data\:set\:contains\:the\:values\:}a_1,\:\ldots \:,\:a_n\mathrm{\:\left(n\:elements\right)\:then\:the\:average}= \\ \frac{\sum x}{n}=\frac{326}{10}=32.6 \end{gathered}[/tex]Step 3
Find the standard deviation
[tex]S\mathrm{tandard\:deviation,\:}\sigma\left(X\right)\mathrm{,\:is\:the\:square\:root\:of\:the\:variance:}\sigma\left(X\right)=\sqrt{\frac{\sum(x_i-\mu)^2}{N}}[/tex][tex]Standard\text{ deviation=}17.28326[/tex]Step 4
Find Q1
[tex]\begin{gathered} The\:first\:quartile\:is\:computed\:by\:taking\:the\:median\:of\:the\:lower\:half\:of\:a\:sorted\:set \\ Arrange\text{ in ascending order} \\ 10,\:15,\:19,\:20,\:25,\:34,\:44,\:47,\:52,\:60 \\ Take\text{ the lower half of the ascending set} \\ 10,15,19,20,25 \\ Q_1=19 \end{gathered}[/tex]Step 5
Find Q3
[tex]\begin{gathered} \mathrm{The\:third\:quartile\:is\:computed\:by\:taking\:the\:median\:of\:the\:higher\:half\:of\:a\:sorted\:set.} \\ Arrange\text{ the terms in ascending order} \\ 10,\:15,\:19,\:20,\:25,\:34,\:44,\:47,\:52,\:60 \\ Take\text{ the upper half of the ascending term} \\ 34,44,47,52,60 \\ Q_3=47 \end{gathered}[/tex]Step 6
Find the lower fence
[tex]\begin{gathered} =Q_1-1.5(IQR) \\ IQR=Q_3-Q_1=47-19=28 \\ =19-1.5(28)=-23 \end{gathered}[/tex]Step 7
Find the upper fence
[tex]\begin{gathered} =Q_3+1.5(IQR) \\ =47+1.5(28)=89 \end{gathered}[/tex]