Chapter 4, Problem 4.1E

To determine

(a)

The percentage of the students $A\text{'}$ and $B\text{'}$ who rarely or never uses sunscreen when going out in sun and identify between row and column percentage

Answer to Problem 4.1E

So, $64.3\%$ of Students making $A\text{'}$ s and $B\text{'}$ s of them rarely and never use sunscreen. And this is row percentage

Explanation of Solution

Given:

Table for sunscreen Use:

Grade	Never or rarely	Sometimes	Always or most times	Total
$A\text{'}$ and $B\text{'}$	$1322$	$450$	$285$	$2057$
$C\text{'}$	$568$	$83$	$47$	$698$
$D\text{'}$ s and $F\text{'}$ s	$85$	$15$	$3$	$103$
Total	$1975$	$548$	$335$	$2858$

Calculation:

In this problem, data shown in given above table is referred, that is describing the usual grades that students get and how often they use screen.

Students who gets $A\text{'}s$ and $B\text{'}s$ of them rarely and never use sunscreen,

  $\frac{NorR}{T}$

Where,

  $NorR=$ no of students who gets $A\text{'}s$ and $B\text{'}s$ from column of Never or rarely used students

  $T=$ no of students who gets $A\text{'}s$ and $B\text{'}s$ from Total column

So,

  $\begin{array}{l}=\frac{NorR}{T}\\ =\frac{1322}{2057}\\ =64.3\%\end{array}$

Thus, $64.3\%$ of Students making $A\text{'}$ s and $B\text{'}$ s of them rarely and never use sunscreen. And this is row percentage as due to focusing on the only one $1^{st}$ row corresponding to the $A\text{'}$ s and $B\text{'}$ s at the time when calculating the percentage

Conclusion:

Therefore, $64.3\%$ of Students who gets $A\text{'}$ s and $B\text{'}$ s of them rarely and never use sunscreen. And this is row percentage

To determine

(b)

The percentage of students who wear sunscreen who gets $C\text{'}$ and identify between row and column percentage.

Answer to Problem 4.1E

So, $15.1\%$ of Students who gets $C\text{'}s$ of them sometimes use sunscreen. And this is column percentage.

Explanation of Solution

Given:

Table for sunscreen Use:

Grade	Never or rarely	Sometimes	Always or most times	Total
$A\text{'}$ and $B\text{'}$	$1322$	$450$	$285$	$2057$
$C\text{'}$	$568$	$83$	$47$	$698$
$D\text{'}$ s and $F\text{'}$ s	$85$	$15$	$3$	$103$
Total	$1975$	$548$	$335$	$2858$

Calculation:

In this problem, data shown in given above table is referred, that is describing the usual grades that students get and how often they use screen.

Students making $C\text{'}s$ of them sometimes wear a sunscreen,

  $C\text{'}s=\frac{S}{T_s}$

Where,

  $S=$ no of students who gets $C\text{'}s$ from column of sometimes

  $T_s=$ Total of sometimes column.

So,

  $\begin{array}{l}=\frac{S}{T_s}\\ =\frac{83}{548}\\ =15.1\%\end{array}$

Thus, $15.1\%$ of Students who gets $C\text{'}s$ of them sometimes use sunscreen. And this is column percentage as due to focusing on the only on the $2^{nd}$ column (corresponding to the sometimes-wearing sunscreen) at the time when calculating the percentage.

Conclusion:

Therefore, $15.1\%$ of Students who gets $C\text{'}s$ of them sometimes use sunscreen. And this is column percentage.

To determine

(c)

The percentage of overall sample who gets $A\text{'}$ s and $B\text{'}$ s in school and uses sunscreen always or most times.

Answer to Problem 4.1E

No of Students who gets $A\text{'}sorB\text{'}s$ of them use sunscreen always or most of the times is the $10\%$

Explanation of Solution

Given:

Table for sunscreen Use:

Grade	Never or rarely	Sometimes	Always or most times	Total
$A\text{'}$ and $B\text{'}$	$1322$	$450$	$285$	$2057$
$C\text{'}$	$568$	$83$	$47$	$698$
$D\text{'}$ s and $F\text{'}$ s	$85$	$15$	$3$	$103$
Total	$1975$	$548$	$335$	$2858$

Calculation:

In this problem, data shown in given above table is referred, that is describing the usual grades that students get and how often they use screen.

The number of students who usually get $A\text{'}$ s and $B\text{'}$ s and who also always or usually wear sunscreen is the no in the corresponding cell.

So, overall sample who gets $A\text{'}$ s and $B\text{'}$ s is,

The percentage of students making $C\text{'}s$ of them sometimes wear a sunscreen,

  $C\text{'}s=\frac{AorM}{T}$

Where,

  $AorM=$ Students who get $A\text{'}$ s and $B\text{'}$ s is from always or most times column.

  $T_s=$ Total.

So,

  $\begin{array}{l}A\text{'}sorB\text{'}s=\frac{AorM}{T}\\ =\frac{285}{2858}\\ =10\%\end{array}$

Thus, no of Students who gets $A\text{'}sorB\text{'}s$ of them use sunscreen always or most of the times is the $10\%$

Conclusion:

Therefore, no of Students who gets $A\text{'}sorB\text{'}s$ of them use sunscreen always or most of the times is the $10\%$

To determine

(d)

The complete table of row percentages.

Answer to Problem 4.1E

The complete table of row percentage is given as below:

Grade	Never or rarely	Sometimes	Always or most times	Total
$A\text{'}$ and $B\text{'}$	$1322\left(64.3\%\right)$	$450\left(21.9\%\right)$	$285\left(13.9\%\right)$	$2057$
$C\text{'}$	$568\left(81.4\%\right)$	$83\left(11.9\%\right)$	$47\left(6.7\%\right)$	$698$
$D\text{'}$ s and $F\text{'}$ s	$85\left(82.5\%\right)$	$15\left(14.6\%\right)$	$3\left(2.9\%\right)$	$103$
Total	$1975\left(69.1\%\right)$	$548\left(19.2\%\right)$	$335\left(11.2\%\right)$	$2858$

Explanation of Solution

Given:

Table for sunscreen use:

Grade	Never or rarely	Sometimes	Always or most times	Total
$A\text{'}$ and $B\text{'}$	$1322$	$450$	$285$	$2057$
$C\text{'}$	$568$	$83$	$47$	$698$
$D\text{'}$ s and $F\text{'}$ s	$85$	$15$	$15$	$103$
Total	$1975$	$548$	$548$	$2858$

Calculation:

In this problem, data shown in given above table is referred, that is describing the usual grades that students get and how often they use screen.

And the complete table of row percentage is given as below:

Grade	Never or rarely	Sometimes	Always or most times	Total
$A\text{'}$ and $B\text{'}$	$1322\left(64.3\%\right)$	$450\left(21.9\%\right)$	$285\left(13.9\%\right)$	$2057$
$C\text{'}$	$568\left(81.4\%\right)$	$83\left(11.9\%\right)$	$47\left(6.7\%\right)$	$698$
$D\text{'}$ s and $F\text{'}$ s	$85\left(82.5\%\right)$	$15\left(14.6\%\right)$	$3\left(2.9\%\right)$	$103$
Total	$1975\left(69.1\%\right)$	$548\left(19.2\%\right)$	$335\left(11.2\%\right)$	$2858$

In each cell, the row percentage was calculated by dividing the cell's value with the total no of students in the same row.

For example, in the cell for sometimes and $C\text{'}s$, divide the cell's value $\left(83\right)$ by the total no of students in the $C\text{'}s$ row, $698$

Conclusion:

The complete table of row percentage is given as below:

Grade	Never or rarely	Sometimes	Always or most times	Total
$A\text{'}$ and $B\text{'}$	$1322\left(64.3\%\right)$	$450\left(21.9\%\right)$	$285\left(13.9\%\right)$	$2057$
$C\text{'}$	$568\left(81.4\%\right)$	$83\left(11.9\%\right)$	$47\left(6.7\%\right)$	$698$
$D\text{'}$ s and $F\text{'}$ s	$85\left(82.5\%\right)$	$15\left(14.6\%\right)$	$3\left(2.9\%\right)$	$103$
Total	$1975\left(69.1\%\right)$	$548\left(19.2\%\right)$	$335\left(11.2\%\right)$	$2858$

To determine

(e)

Explanation of percentage found in part 'd'.

Answer to Problem 4.1E

The row percentages found in part 'd' indicates that there is some relationship between the usual grades of the students and how often they apply sunscreens.

Explanation of Solution

Given:

Table for sunscreen Use:

Grade	Never or rarely	Sometimes	Always or most times	Total
$A\text{'}$ and   $B\text{'}$	$1322$	$450$	$285$	$2057$
$C\text{'}$	$568$	$83$	$47$	$698$
$D\text{'}$ s and   $F\text{'}$ s	$85$	$15$	$15$	$103$
Total	$1975$	$548$	$548$	$2858$

Calculation:

The row percentages found in part 'iv' indicates that there is some relationship between the usual grades of the students and how often they apply sunscreens.

For example, students who gets $A\text{'}sorB\text{'}s$, $13.9\%$ of students always or most of the time apply sunscreen.

Yet for students who usually get $D\text{'}s$ and $F\text{'}s$ only, $2.9\%$ of these students apply sunscreen most of the time or always. This suggest the distribution of different for $A$ or $B$ students than its for $D$ or $F$ students.

Conclusion:

The row percentages found in part 'iv' indicates that there is some relationship between the usual grades of the students and how often they apply sunscreens.