Chapter 13.2, Problem 16E

To determine

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

Answer to Problem 16E

  $Mean=33.3,Median=32,Mode=30,32$ .

Explanation of Solution

Given information:

The given data set is $30,37,32,39,30,34,32,30,32,37$

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 $30,37,32,39,30,34,32,30,32,37$ .

So,

  $\begin{array}{l}Mean=\frac{\text{Sum of all observations}}{\text{Total number of observations}}\\ Mean=\frac{30+37+32+39+30+34+32+30+32+37}{10}=\frac{333}{10}=33.3\end{array}$

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

  $30,30,30,32,32,32,34,37,37,39$

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

  $Median=\frac{32+32}{2}=32$

And as we see, 30 and 32 occurs the most frequent times, so the data set has two modes $30\text{ and }32$ .

Conclusion:

  $Mean=33.3,Median=32,Mode=30,32$