Chapter 13.2, Problem 13E

To determine

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

Answer to Problem 13E

  $Mean=10.5,Median=8.5,Mode=7,12$ .

Explanation of Solution

Given information:

The given data set is $5,12,7,24,8,9,7,12$

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 $5,12,7,24,8,9,7,12$

So,

  $\begin{array}{l}Mean=\frac{\text{Sum of all observations}}{\text{Total number of observations}}\\ Mean=\frac{5+12+7+24+8+9+7+12}{8}=\frac{84}{8}=10.5\end{array}$

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

  $5,7,7,8,9,12,12,24$

And as the numbers in data is even, so median is the average of middle two numbers. So,

  $Median=\frac{8+9}{2}=\frac{17}{2}=8.5$

And as we see, 7 and 12 occur the most frequent times, so the data set has two modes $7\text{}\text{ and 12}$

Conclusion:

  $Mean=10.5,Median=8.5,Mode=7,12$