Chapter 14.1, Problem 12E

(a)

To determine

To find: the range of the heights of the buildings.

Answer to Problem 12E

The range is $619$ .

Explanation of Solution

Given:

Height of the tallest building in united states are:

  $404,405,440,450,471,500,535,546,579,626,697,714,738,739,871,943,945,1000,1018,1023$

Concept used:

  $\text{Range=highest value-lowest value}\text{.}$

Calculation:

According to the given in Ascending order is:

  $404,405,440,450,471,500,535,546,579,626,697,714,738,739,871,943,945,1000,1018,1023$ .

To calculate the range of a set of data, subtract the lowest value from highest value.

  $\begin{array}{l}\text{Range=highest value-lowest value}\text{.}\\ \text{Range=102}3-404=619.\end{array}$

Hence, the range is $619$ .

(b)

To determine

To find: the appropriate class intervals of height of the buildings.

Answer to Problem 12E

Class interval is $\text{105}$ .

Explanation of Solution

Given:

Height of the tallest building in united states are:

  $404,405,440,450,471,500,535,546,579,626,697,714,738,739,871,943,945,1000,1018,1023$ .

Concept used:

  $\text{Class interval=}\frac{\text{range}}{\text{divisibe of range}}$ .

Calculation:

According to the given in Ascending order is:

  $404,405,440,450,471,500,535,546,579,626,697,714,738,739,871,943,945,1000,1018,1023$ .

Class interval can be found by:

There are $6$ intervals of $105$ .

Hence, class interval is $\text{105}$ .

(c)

To determine

To construct: the frequency distribution table for the given heights of the building.

Answer to Problem 12E

From the frequency distribution tables the frequency can be calculated and total frequency is $20$ .

Explanation of Solution

Given:

Height of the tallest building in united states are:

  $404,405,440,450,471,500,535,546,579,626,697,714,738,739,871,943,945,1000,1018,1023$ .

Concept used:

The frequency distribution table consist of frequency and tally marks which can easily measure the range class limits class size by looking at their respective blocks.

Calculation:

According to the given in Ascending order is:

  $404,405,440,450,471,500,535,546,579,626,697,714,738,739,871,943,945,1000,1018,1023$

The frequencies distribution table:

Height in feet	Frequency Tally marks	frequency
$404-509$	||||	$5$
$509-614$	|||	$3$
$614-719$	||||	$4$
$719-824$	||	$2$
$824-929$	|	$1$
$929-1034$	||||	$5$
Total		$20$

Hence, from the frequency distribution table the frequency can be calculated and total frequency is $20$ .

(d)

To determine

To Graph: the frequency polygon of the heights of the building.

Answer to Problem 12E

From the frequency polygon its more cleared that mention the maximum and minimum frequency through which range can be solved.

Explanation of Solution

Given:

Height of the tallest building in united states are:

  $404,405,440,450,471,500,535,546,579,626,697,714,738,739,871,943,945,1000,1018,1023$ .

Concept used:

The frequency polygons are graphical device for understanding the shapes of distributions.

The graphing device as same as histogram but specially, helpful for comparing sets of data.

Frequency polygons are also good for displaying cumulative frequency distribution.

Calculation:

According to the given in Ascending order is:

  $404,405,440,450,471,500,535,546,579,626,697,714,738,739,871,943,945,1000,1018,1023$ .

The frequency polygon of the data is:

  

Hence, from the frequency polygon its more cleared that mention the maximum and minimum frequency through which range can be solved.

(e)

To determine

To find: interval which represent the greatest number of the buildings.

Answer to Problem 12E

The intervals are $404-509$ and $929-1034$ .

Explanation of Solution

Given:

Height of the tallest building in united states are:

  $404,405,440,450,471,500,535,546,579,626,697,714,738,739,871,943,945,1000,1018,1023$ .

Concept used:

The interval which has maximum of number of building can be known through highest frequency on the interval.

More is the frequency here means more is the number of buildings.

Calculation:

According to the given in Ascending order is:

  $404,405,440,450,471,500,535,546,579,626,697,714,738,739,871,943,945,1000,1018,1023$ .

The intervals $404-509$ and $929-1034$ .

These intervals have the most building heights in them.

Hence, the intervals are $404-509$ and $929-1034$ .