Chapter B.1, Problem 12E

To determine

To find: The frequency distribution and a histogram to organize the data.

Answer to Problem 12E

The frequency distribution table and histogram are given below.

Explanation of Solution

Given information:

The given data shows the number of students enrolled in the $50$ states and district of Columbia in $2012$ .

$\begin{array}{l}\text{AK}128\\ \text{CA}6185\\ \text{DE}131\\ \text{IA}501\\ \text{KS}486\\ \text{MD}860\\ \text{MO}907\\ \text{ND}99\\ \text{NM}334\\ \text{OK}673\\ \text{SC}683\\ \text{UT}601\\ \text{WI}872\end{array}$

$\begin{array}{l}\text{AL}736\\ \text{CO}869\\ \text{FL}2681\\ \text{ID}294\\ \text{KY}659\\ \text{ME}185\\ \text{MS}493\\ \text{NE}303\\ \text{NV}478\\ \text{OR}564\\ \text{SD}\text{127}\\ \text{VA}1266\\ \text{WV}282\end{array}$

$\begin{array}{l}\text{AR}472\\ \text{CT}550\\ \text{GA}\text{1703}\\ \text{IL}2084\\ \text{LA}708\\ \text{MI}1544\\ \text{MT}\text{143}\\ \text{NH}\text{189}\\ \text{NY}2590\\ \text{PA}\text{1739}\\ \text{TN}980\\ \text{VT}8\text{2}\\ \text{WY}9\text{1}\end{array}$

$\begin{array}{l}\text{AZ}1070\\ \text{DC}76\\ \text{HI}\text{177}\\ \text{IN}\text{1031}\\ \text{MA}954\\ \text{MN}84\text{3}\\ \text{NC}\text{1488}\\ \text{NJ}1358\\ \text{OH}\text{1868}\\ \text{RI}\text{134}\\ \text{TX}5059\\ \text{WA}1053\end{array}$

To begin constructing a frequency distribution, you must first decide on the number of intervals.

The least number is $76$ and the greatest is $6185$ ,it seems that thirteen intervals would be appropriate.

By tallying the data into six intervals, you obtained the frequency distribution shown below.

Interval	Number
$\left[0,500\right)$	20
$\left[500,1000\right)$	16
$\left[1000,1500\right)$	6
$\left[1500,2000\right)$	4
$\left[2000,2500\right)$	1
$\left[2500,3000\right)$	2
$\left[3000,3500\right)$
$\left[3500,4000\right)$
$\left[4000,4500\right)$
$\left[4500,5000\right)$
$\left[5000,5500\right)$	1
$\left[5500,6000\right)$
$\left[6000,6500\right)$	1

The histogram for the table is given as:

  

Therefore, the frequency distribution table and histogram are given above.