Chapter 11.1, Problem 31E

(a)

To determine

To find which Team win the match.

Answer to Problem 31E

Team A wins the match because it has greater mean than Team B.

If Team with greater median will win, then Team B wins.

Explanation of Solution

Given information: Team A Score: $172,130,173,212$ and Team B Score: $136,184,168,192$Formula Used: Mean = $\frac{Sumofallobservations}{Totalobservations}$ and Median = $\frac{{\left(\frac{n}{2}\right)}^{th}+{\left(\frac{n}{2}+1\right)}^{th}}{2}term$

Calculation:

A) Team A:

Team A Score: $172,130,173,212$

So, In Ascending Order

Team A Score: $130,172,173,212$

• Mean

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

So,

Mean = $\frac{130+172+173+212}{4}$

Now,

Mean = $\frac{687}{4}$

Hence,

Mean = $171.75$

• Median

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

So,

Median = $\frac{{\left(\frac{4}{2}\right)}^{th}+{\left(\frac{4}{2}+1\right)}^{th}}{2}term$

Now,

Median = $\frac{{\left(2\right)}^{nd}+{\left(3\right)}^{rd}}{2}term$

As, ${\left(2\right)}^{nd}term=172$ and ${\left(3\right)}^{rd}term=173$

So,

Median = $\frac{172+173}{2}$

Hence,

Median = $172.5$

B) Team B:

Team B Score: $136,184,168,192$

So, In Ascending Order

Team B Score: $136,168,184,192$

• Mean

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

So,

Mean = $\frac{136+168+184+192}{4}$

Now,

Mean = $\frac{680}{4}$

Hence,

Mean = $170$

• Median

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

So,

Median = $\frac{{\left(\frac{4}{2}\right)}^{th}+{\left(\frac{4}{2}+1\right)}^{th}}{2}term$

Now,

Median = $\frac{{\left(2\right)}^{nd}+{\left(3\right)}^{rd}}{2}term$

As, ${\left(2\right)}^{nd}term=168$ and ${\left(3\right)}^{rd}term=184$

So,

Median = $\frac{168+184}{2}$

Hence,

Median = $176$

So,

Team A wins the match because it has greater mean than Team B.

Now,

If Team with greater median will win, then Team B wins.

(b)

To determine

To find which Team is more consistent.

Answer to Problem 31E

Team A.

Explanation of Solution

Given information: Team A: Mean = $171.75$ , Median = $172.5$ and Team B: Mean = $170$ , Median = $176$

Calculation:

Team A: Mean = $171.75$ , Median = $172.5$

And

Team B: Mean = $170$ , Median = $176$

So,

Mean and Median values of Team A are much similar than Team B.

Hence,

Team A is more consistent.

(c)

To determine

To find which Team win the match.

Answer to Problem 31E

Team B wins the match because it has greater mean than Team A.

Explanation of Solution

Given information: Team A Score: $172,130,173,212$ and Team B Score: $136,184,168,192$

Team A score increase by 15 and Team B score increase by 12.5%

Formula Used: Mean = $\frac{Sumofallobservations}{Totalobservations}$

Calculation:

A) Team A:

Team A Score: $172,130,173,212$

As,

Team A score increase by 15

Now,

Team A Score: $187,145,188,227$

• Mean

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

So,

Mean = $\frac{187+145+188+227}{4}$

Now,

Mean = $\frac{747}{4}$

Hence,

Mean = $186.75$

B) Team B:

Team B Score: $136,184,168,192$

As,

Team B score increase by 12.5%

Now,

Team B Score: $153,207,189,216$

• Mean

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

So,

Mean = $\frac{153+207+189+216}{4}$

Now,

Mean = $\frac{765}{4}$

Hence,

Mean = $191.25$

So,

Team B wins the match because it has greater mean than Team A.