Chapter 13.2, Problem 15E

To determine

To Calculate: The mean, median and mode of the given data set.

Answer to Problem 15E

  $Mean=8.11,Median=7,Mode=7$ .

Explanation of Solution

Given information:

The given data set is $5,6,12,7,14,9,7,7,6$

Concept and Formula Used:

We use the concept of mean, median and mode.

Mean: The mean of n numbers is the sum of the numbers divided by n.

Median: The median is the middle number when the numbers are written in order. When n is even, median is the average of middle two numbers.

Mode: The number that occurs most frequently is called the mode. When two numbers tie for most frequent occurrence, the collection has two modes and is called bimodal.

Calculation:

The given data set is The given data set is $5,6,12,7,14,9,7,7,6$

So,

  $\begin{array}{l}Mean=\frac{\text{Sum of all observations}}{\text{Total number of observations}}\\ Mean=\frac{5+6+12+7+14+9+7+7+6}{9}=\frac{73}{9}=8.11\end{array}$

Now, for median we arrange the data set in increasing order, so we get

  $5,6,6,7,7,7,9,12,14$

And as the numbers in data is odd, so median is the middle number. So,

  $Median=7$

And as we see, 7 occurs the most frequent times, so the data set hasmode $7\text{}$ .

Conclusion:

  $Mean=8.11,Median=7,Mode=7$