Question

For this question it is asking for the mean, standard deviation, Q1, Q3, lower fence, and upper fence

Answer 1

Step 1

Given;

`10,\:15,\:19,\:52,\:34,\:44,\:47,\:20,\:60,\:25`

Step 2

Find the mean

`\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}= \\ (\sum x)/(n)=(326)/(10)=32.6 \end{gathered}`

Step 3

Find the standard deviation

`S\mathrm{tandard\:deviation,\:}\sigma\left(X\right)\mathrm{,\:is\:the\:square\:root\:of\:the\:variance:}\sigma\left(X\right)=\sqrt{(\sum(x_i-\mu)^2)/(N)}`
`Standard\text{ deviation=}17.28326`

Step 4

Find Q1

`\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}`

Step 5

Find Q3

`\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}`

Step 6

Find the lower fence

`\begin{gathered} =Q_1-1.5(IQR) \\ IQR=Q_3-Q_1=47-19=28 \\ =19-1.5(28)=-23 \end{gathered}`

Step 7

Find the upper fence

`\begin{gathered} =Q_3+1.5(IQR) \\ =47+1.5(28)=89 \end{gathered}`