Chapter 12.2, Problem 28PPS

a.

To determine

To duplicate the given stacks with coins.

Answer to Problem 28PPS

The duplicated stacks with coin are obtained as:

  

Explanation of Solution

Given information :

the distribution of the coins in unequal stacks is given as:

  

Total number of coins is:

  $2+3+3+4+5+6+6+8+8=45$

So, set up 45 coins in the given ordered allocation.

Now,

Duplicate the stacks with coins and arrange the stacks of coins on the paper above the number that corresponds to height of each stack.

  

b.

To determine

To make a line plot of the stacks.

Answer to Problem 28PPS

The line plot of the stacks is:

  

Explanation of Solution

Given information :

the distribution of the coins in unequal stacks is given as:

  

Total number of coins is:

  $2+3+3+4+5+6+6+8+8=45$

So, set up 45 coins in the given ordered allocation.

Now,

Duplicate the stacks with coins and arrange the stacks of coins on the paper above the number that corresponds to height of each stack.

  

To form the line plot, replace each of the stacks with an dot.

The line plot of the stacks is obtained as:

  

c.

To determine

To move the coins one at a time to make the stacks equal.

Answer to Problem 28PPS

the number of moves required to change the stacks of unequal coins to the stacks of equal coins is 4.

Explanation of Solution

Given information :

the distribution of the coins in unequal stacks is given as:

  

Total number of coins is:

  $2+3+3+4+5+6+6+8+8=45$

Setup 45 coins in 5 equal stacks. Each stacks contains 9 coin.

Move the two stacks of 3 coins to two stacks of 6 coins. So, 2 stacks of 9 coins is made.

Then move a stack of 4 coins to a stake of 5 coins. So, one stacks of 9 coins is made.

And lastly, move one coin from the stack of 2 coins to one stack of 8 coins and remaining one coin from the stack of 2 coins to another stack of 8 coins.

So, the number of moves required to change the stacks of unequal coins to the stacks of equal coins is 4.

The original set of stacks contain 9 stacks of unequal coins. By performing 4 moves as stated above the original stacks is changed to a new set of stacks which contain 5 stacks of 9 coins each which is equal to the number of stacks in original set of stack minus number of moves required to change the stacks of unequal coins to the stacks of equal coins.

d.

To determine

To find the mean of the absolute values of the set of stacks of coins.

Answer to Problem 28PPS

the mean of the absolute values of the set of stacks of coins is 5.

Explanation of Solution

Given information :

the distribution of the coins in unequal stacks is given as:

  

Total number of coins is:

  $2+3+3+4+5+6+6+8+8=45$

The original set of stacks contain 9 stacks of unequal coins.

So the mean of absolute values of set of stacks of coin is obtained as:

  $\frac{2+3+3+4+5+6+6+8+8}{9}=5$

Hence,

The mean of the absolute values of the set of stacks of coins is 5 and this value describe that the new set of stacks of equal coins contain 5 stacks each of which contain 9 coins.