Chapter 11.1, Problem 10E

(a)

To determine

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

Answer to Problem 10E

Mean = $-0.4$

Median = $0.86$

No Mode

Explanation of Solution

Given information: $1.05,2.03,-13.78,-2.41,2.64,0.67,4.02,1.39,0.66,-0.28,-3.01,2.20$

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

Calculation:

  $1.05,2.03,-13.78,-2.41,2.64,0.67,4.02,1.39,0.66,-0.28,-3.01,2.20$

Now, in Ascending Order

  $-13.78,-3.01,-2.41,-0.28,0.66,0.67,1.05,1.39,2.03,2.20,2.64,4.02$

• Mean

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

So,

Mean = $\frac{-13.78-3.01-2.41-0.28+0.66+0.67+1.05+1.39+2.03+2.20+2.64+4.02}{12}$

Now,

Mean = $\frac{-19.48+14.66}{12}$

So,

Mean = $\frac{-4.82}{12}$

Hence,

Mean = $-0.4$

• Median

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

So,

Median = $\frac{{\left(\frac{12}{2}\right)}^{th}+{\left(\frac{12}{2}+1\right)}^{th}}{2}term$

Now,

Median = $\frac{{\left(6\right)}^{th}+{\left(7\right)}^{th}}{2}term$

As, ${\left(6\right)}^{th}term=0.67$ and ${\left(7\right)}^{th}term=1.05$

So,

Median = $\frac{0.67+1.05}{2}$

Hence,

Median = $0.86$

• Mode

Mode = Most repeated value.

So,

No Mode as no repeated value

(b)

To determine

To find measure of center best represents of data.

Answer to Problem 10E

Median

Explanation of Solution

Given information: Mean, Median and Mode

Calculation:

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

(c)

To determine

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

Answer to Problem 10E

Mean = $-0.04$

Median = $1.05$

No Mode

Explanation of Solution

Given information: $1.05,2.03,-13.78,-2.41,2.64,0.67,4.02,1.39,0.66,-0.28,-3.01,2.20,4.28$

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

Calculation:

  $1.05,2.03,-13.78,-2.41,2.64,0.67,4.02,1.39,0.66,-0.28,-3.01,2.20,4.28$

Now, in Ascending Order

  $-13.78,-3.01,-2.41,-0.28,0.66,0.67,1.05,1.39,2.03,2.20,2.64,4.02,4.28$

• Mean

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

So,

Mean = $\frac{-13.78-3.01-2.41-0.28+0.66+0.67+1.05+1.39+2.03+2.20+2.64+4.02+4.28}{13}$

Now,

Mean = $\frac{-19.48+18.94}{13}$

So,

Mean = $\frac{-0.54}{13}$

Hence,

Mean = $-0.04$

• Median

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

So,

Median = ${\left(\frac{13+1}{2}\right)}^{th}term$

Now,

Median = ${\left(7\right)}^{th}term$

As, ${\left(7\right)}^{th}term=1.05$

Hence,

Median = $1.05$

• Mode

Mode = Most repeated value.

So,

No Mode as no repeated value