Chapter 13.2, Problem 68E

To determine

To construct: A set of numbers that have the given measures of central tendency.

Answer to Problem 68E

The set of numbers is $\left\{3,4,4,4,15\right\}$ .

Explanation of Solution

Given:

Mean is 6, Median is 4 and Mode is 4.

Calculation:

Base on the given measures, there can be many possible sets. One such set is determined as shown below:

1) Given that the mean is 6, the average of the numbers should be equal to 6.

2) For the median to be 4, the center value should be 4 when the data is arranged either is ascending or descending order. Assume that the data is arranged in ascending order and for convenience point of view, let there be 5 numbers, out of which the 3^rd number is 4.

3) To determine the other 4 numbers, the value of mode proves to be further useful. Since mode is the most frequently occurring number, let 4 be repeated a total of 3 times. So now all is left to determine the remaining 2 numbers in the data set. Let those be represented by x and y.

By point 1,

  $\begin{array}{c}\frac{x+4+4+4+y}{5}=6\\ x+y+12=30\\ x+y=18\end{array}$

Since the data is arranged in an ascending order, the value for x has to be less than 4. So, x can take the values 1, 2 or 3. Let $x=3$ . Then $y=15$ .

So, the data set is $\left\{3,4,4,4,15\right\}$ .