Chapter 11.1, Problem 8E

(a)

To determine

To find the mean, median and mode of data set.

Answer to Problem 8E

Mean = $13.2$

Median = $14.5$

Mode = 14 and 15

Explanation of Solution

Given information: $14,15,3,15,14,14,18,15,8,16$

Formula Used: Mean = $\frac{Sumofallobservations}{Totalobservations}$ , Median = ${\left(\frac{n+1}{2}\right)}^{th}term$ , Mode = Most repeated value.

Calculation:

  $14,15,3,15,14,14,18,15,8,16$

Now, in Ascending Order

  $3,8,14,14,14,15,15,15,16,18$

• Mean

Mean = $\frac{Sumofallobservations}{Totalobservations}$

So,

Mean = $\frac{3+8+14+14+14+15+15+15+16+18}{10}$

Now,

Mean = $\frac{132}{10}$

Hence,

Mean = $13.2$

• Median

Median for even numbers = $\frac{{\left(\frac{n}{2}\right)}^{th}+{\left(\frac{n}{2}+1\right)}^{th}}{2}term$

So,

Median = $\frac{{\left(\frac{10}{2}\right)}^{th}+{\left(\frac{10}{2}+1\right)}^{th}}{2}term$

Now,

Median = $\frac{{\left(5\right)}^{th}+{\left(6\right)}^{th}}{2}term$

As, ${\left(5\right)}^{th}term=14$ and ${\left(6\right)}^{th}term=15$

So,

Median = $\frac{14+15}{2}$

Hence,

Median = $14.5$

• Mode

Mode = Most repeated value.

So,

14 and 15 is the most repeated value.

Mode = 14 and 15

(b)

To determine

To find measure of center best represents of data.

Answer to Problem 8E

Median

Explanation of Solution

Given information: Mean, Median and Mode

Calculation:

Median best describes the central tendency data because the outlier disturbs the mean.