Chapter 11.1, Problem 9E

(a)

To determine

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

Answer to Problem 9E

Mean = $1.96$

Median = $2$

Mode = $1\frac{2}{3}$ and $2$

Explanation of Solution

Given information: $1\frac{1}{3},1\frac{2}{3},2,3,2\frac{1}{3},1\frac{2}{3},2,2,1\frac{2}{3}$

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

Calculation:

  $1\frac{1}{3},1\frac{2}{3},2,3,2\frac{1}{3},1\frac{2}{3},2,2,1\frac{2}{3}$

Now, in Ascending Order

  $1\frac{1}{3},1\frac{2}{3},1\frac{2}{3},1\frac{2}{3},2,2,2,2\frac{1}{3},3$

• Mean

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

So,

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

Now,

Mean = $\frac{\frac{26}{3}+9}{9}$

So,

Mean = $\frac{\frac{26+27}{3}}{9}$

Now,

Mean = $\frac{53}{27}$

Hence,

Mean = $1.96$

• 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, ${\left(5\right)}^{th}term=2$

Hence,

Median = $2$

• Mode

Mode = Most repeated value.

So,

  $1\frac{2}{3}$ and $2$ is the most repeated value.

Mode = $1\frac{2}{3}$ and $2$

(b)

To determine

To find measure of center best represents of data.

Answer to Problem 9E

Mean

Explanation of Solution

Given information: Mean, Median and Mode

Calculation:

Mean best describes the central tendency.