Question

find the lower quartile of -4, 5, 6, 9

Answer 1

Answer:

$\mathrm{First\:Quartile\:\left(lower\:quartile\right)\:of\:}-4,\:5,\:6,\:9:\quad 0.5$

Step-by-step explanation:

$\mathrm{First\:Quartile}$

The first quartile is the value separating the lower quarter and higher three-quarters of the data set.

The first quartile is computed by taking the median of the lower half of a sorted set.

$\mathrm{Arrange\:the\:terms\:in\:ascending\:order}$

$-4,\:5,\:6,\:9$

$\mathrm{Take\:the\:lower\:half\:of\:the\:ascending\:set}$

$\mathrm{Count\:the\:number\:of\:terms\:in\:the\:data\:set}$

$\begin{Bmatrix}-4&5&6&9\\ 1&2&3&4\end{Bmatrix}$

$\mathrm{The\:number\:of\:terms\:in\:the\:data\:set\:is}$

$4$

$\mathrm{Take\:the\:lower\:}2\mathrm{\:terms}$

$-4,\:5$

$\mathrm{Median\:of\:}-4,\:5$

$\mathrm{Median}$

• The median is the value separating the higher half of the data set, from the lower half.
• If the number of terms is odd, then the median is the middle element of the sorted set
• If the number of terms is even, then the median is the arithmetic mean of the two middle elements of the sorted set

$\mathrm{Arrange\:the\:terms\:in\:ascending\:order}$

$-4,\:5$

$\mathrm{Find\:the\:median\:of\:the\:ascending\:set}$

$\mathrm{Count\:the\:number\:of\:terms\:in\:the\:data\:set}$

$\begin{Bmatrix}-4&5\\ 1&2\end{Bmatrix}$

$\mathrm{The\:number\:of\:terms\:in\:the\:data\:set\:is}$

$2$

$\mathrm{Since\:the\:number\:of\:terms\:is\:even,\:the\:median\:is\:the\:average\:of\:the\:two\:middle\:elements:\quad }-4,\:5$

$\mathrm{Arithmetic\:Mean\:\left(average\right)\:of\:}-4,\:5$

$\mathrm{Arithmetic\:Mean}$

• The arithemtic mean (average) is the sum of the values in the set divided by the number of elements in that set.
• If our data set contains the values $a_1,\:\ldots \:,\:a_n$ (n elements) then the average $=\dfrac{1}{n}\displaystyle\sum _{i=1}^na_i$

$\mathrm{Compute\:the\:sum\:of\:the\:data\:set}$

$\mathrm{Take\:the\:sum\:of\:}-4,\:5$

$-4+5$

Simplify

$1$

$\mathrm{Compute\:the\:number\:of\:terms\:in\:the\:data\:set}$

$\mathrm{Count\:the\:number\:of\:terms\:in\:the\:data\:set}$

$\begin{Bmatrix}-4&5\\ 1&2\end{Bmatrix}$

$\mathrm{The\:number\:of\:terms\:in\:the\:data\:set\:is}$

$2$

$\mathrm{Divide\:the\:sum\:by\:the\:number\:of\:terms\:and\:simplify}$

$\mathrm{Divide\:the\:sum\:by\:the\:number\:of\:terms:\quad }\dfrac{\displaystyle\sum _{i=1}^na_i}{n}=\dfrac{1}{2}$

$\mathrm{Simplify}$

$0.5$