Chapter 10.8, Problem 29CCR

a.

To determine

To find: The median of fat games in each sandwich.

Answer to Problem 29CCR

Median of chicken $=15$ , Median of burgers $=23$ .

Explanation of Solution

Given Information: A table containing food data is given.

Calculation:

Median of chicken:

Here, n = Q

  $\begin{array}{l}M=\frac{\frac{n}{2}th\text{value}+(\frac{n}{2}+1)th\text{value}}{2}\\ =\frac{\frac{Q}{2}th\text{value}+(\frac{Q}{2}+1)th\text{value}}{2}\\ =\frac{4th\text{value}+5th\text{value}}{2}\\ =\frac{15+15}{2}=\frac{30}{2}\\ =15\end{array}$

Median of burger:

Here n = Q

  $\begin{array}{l}M=\frac{\frac{n}{2}th\text{value}+(\frac{n}{2}+1)th\text{value}}{2}\\ =\frac{\frac{Q}{2}th\text{value}+(\frac{Q}{2}+1)th\text{value}}{2}\\ =\frac{4th\text{value}+5th\text{value}}{2}\\ =\frac{20+26}{2}=\frac{46}{2}\\ =23\end{array}$

Median of chicken $=15$ , Median of burgers $=23$ .

b.

To determine

To find: The type of sandwich having a lower amount of fat.

Answer to Problem 29CCR

Explanation of Solution

Given Information: A table containing food data is given.

Most veggie burgers contains from zero to 1 gram of saturated fat.

A burger made of extra lean ground beef (90% lean) reduce saturated fat, but only to three to five gram chicken, turkey and salmon burger are better option at two to three grams, their saturated fat can be almost as low as a veggie burgers.

Coefficient of variation:

  $\begin{array}{l}{v}_x=\frac{f_x}{x}=\frac{3.67}{15.12}=0.24\\ v_y=\frac{f_y}{y}=\frac{8.59}{23.62}=0.36\end{array}$

The outliers of data is 8.

c.

To determine

To calculate: The measures of variability and any outliers for the data.

Answer to Problem 29CCR

Explanation of Solution

Given Information: A table containing food data is given.

Chicken Burger

x	$x^2$	y	$y^2$
8	64	10	100
13	169	14	196
13	169	20	400
15	225	20	400
15	225	26	676
18	324	31	961
19	361	32	1024
20	400	36	1296
121	1937	189	5053

  $\begin{array}{l}\overline{x}=\frac{\sum x}{n}=\frac{121}{8}\overline{y}=\frac{\sum y}{n}=\frac{189}{8}\\ =15.12=23.62\\ \end{array}$

  $\begin{array}{l}$ f{x}^2=\frac{1}{n}\sum x^2-{(\frac{\sum x}{n})}^{2}f{y}^2=\frac{1}{n}\sum y^2-{(\frac{\sum y}{n})}^2$$ =\frac{1937}{8}-{(15.12)}^2=\frac{5053}{8}-{(23.62)}^2$=242.12-228.61=631.62-557.90\\ =13.51=73.72\\ fx=\sqrt{13.51}fy=\sqrt{73.72}\\ =3.67\%=8.59\%\end{array}$