Chapter 11.1, Problem 5E

(a)

To determine

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

Answer to Problem 5E

Mean = $4$

Median = $3$

Mode = $1$

Explanation of Solution

Given information: $3,5,1,5,1,1,2,3,15$

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

Calculation:

  $3,5,1,5,1,1,2,3,15$

Now, in Ascending Order

  $1,1,1,2,3,3,5,5,15$

• Mean

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

So,

Mean = $\frac{1+1+1+2+3+3+5+5+15}{9}$

Now,

Mean = $\frac{36}{9}$

Hence,

Mean = $4$

• Median

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

So,

Median = ${\left(\frac{9+1}{2}\right)}^{th}term$

Now,

Median = ${\left(5\right)}^{th}term$

As, ${\left(5\right)}^{th}term=3$

Hence,

Median = $3$

• Mode

Mode = Most repeated value.

So,

1 is the most repeated value.

Mode = $1$

(b)

To determine

To find measure of center best represents of data.

Answer to Problem 5E

Median

Explanation of Solution

Given information: Mean, Median and Mode

Calculation:

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