Chapter 14.2, Problem 27E

(a)

To determine

To find: The set of numbers that have mean, median and mode all are the same.

Answer to Problem 27E

The set of numbers is $\left\{9,9,9,9,9\right\}$ .

Explanation of Solution

The set of numbers for that mean, median, and mode all are the same is given as:

  $\left\{9,9,9,9,9\right\}$ .

As the above set fulfils the conditions needed.

(b)

To determine

To find: The set of numbers that have mean is greater than the median.

Answer to Problem 27E

The set of solutions is $\left\{1,2,87\right\}$ .

Explanation of Solution

Consider the set is as:

  $\left\{1,2,87\right\}$

The mean of the set is $30$ and median of the set is $2$ . As the mean is greater than the median, the specified conditions are fulfilled.

(c)

To determine

To find: The set of numbers that have the mode is $10$ and the median is greater than the mean.

Answer to Problem 27E

The set of numbers is $\left\{1,2,10,10,11\right\}$ .

Explanation of Solution

Consider the set of numbers is as:

  $\left\{1,2,10,10,11\right\}$ .

The median and mode of the set of numbers are $10$ , while the mean is 6.8. As the median is greater than the mean, the specified conditions are fulfilled.

(d)

To determine

To find: The set of numbers that have the mean is $6$ ,the median is $5\frac{1}{2}$ , and the mode is $9$ .

Answer to Problem 27E

The mode is $1$ .

Explanation of Solution

Consider the set of numbers is as:

  $\left\{3,4,5,6,9,9\right\}$ .

The mean is $6$ ,the median is $5\frac{1}{2}$ , and the mode is $9$ . As such, the specified conditions are fulfilled.