Chapter 14.1, Problem 10E

(a)

To determine

To find: The range of the grams of fat in various sandwiched served by national fast food restaurants.

Answer to Problem 10E

The range is $49$ .

Explanation of Solution

Given:

The gram of fats:

  $4,5,7,8,9,9,10,12,15,15,15,15,16,18,18,19,20,20,21,22,23,25,27,27,28,29,30,31,31,31,38,39,46,53$

Concept used:

  $\text{Range=highest value-lowest value}\text{.}$

Calculation:

According to the given in Ascending order is:

  $4,5,7,8,9,9,10,12,15,15,15,15,16,18,18,19,20,20,21,22,23,25,27,27,28,29,30,31,31,31,38,39,46,53$

To calculate the range of a set of data, subtract the lowest value from highest value.

  $\begin{array}{l}\text{Range=highest value-lowest value}\text{.}\\ \text{Range=}53-4=49.\end{array}$

Hence, the range is $49$ .

(b)

To determine

To find: the appropriate class intervals of gram of fats.

Answer to Problem 10E

Class interval is $\text{7}$ .

Explanation of Solution

Given:

The gram of fats:

  $4,5,7,8,9,9,10,12,15,15,15,15,16,18,18,19,20,20,21,22,23,25,27,27,28,29,30,31,31,31,38,39,46,53$

Concept used:

  $\text{Class interval=}\frac{\text{range}}{\text{divisibe of range}}$ .

Calculation:

According to the given in Ascending order is:

  $4,5,7,8,9,9,10,12,15,15,15,15,16,18,18,19,20,20,21,22,23,25,27,27,28,29,30,31,31,31,38,39,46,53$

Class interval can be found by:

  $\begin{array}{l}\text{Class interval=}\frac{\text{range}}{\text{divisibe of range}}.\\ \text{Class interval}=\frac{49}{7}=7.\end{array}$

Hence, class interval is $\text{7}$ .

(c)

To determine

To find: the class limit of a gram of fats which are listed below.

Answer to Problem 10E

Class limits are $4,11,18,25,32,39,46\text{ and }53$ .

Explanation of Solution

Given:

The gram of fats:

  $4,5,7,8,9,9,10,12,15,15,15,15,16,18,18,19,20,20,21,22,23,25,27,27,28,29,30,31,31,31,38,39,46,53$

Concept used:

The class limit are lower limit and upper limit.

Intervals of the class is always same.

Calculation:

According to the given in Ascending order is:

  $4,5,7,8,9,9,10,12,15,15,15,15,16,18,18,19,20,20,21,22,23,25,27,27,28,29,30,31,31,31,38,39,46,53$

The class limit are lower limit and upper limit of the class size since, the class size is

  $\text{7}$ and initial value is $4$ therefore the class limits are:

  $\begin{array}{l}4,4+7,4+14,4+21,4+28,+4+35,4+42,4+49.\\ 4,11,18,25,32,39,46\text{ and }53.\end{array}$

Hence, the class limits are $4,11,18,25,32,39,46\text{ and }53$ .

(d)

To determine

To find: The class marks of the gram of fat given below.

Answer to Problem 10E

Class marks are $7.5,14.5,21.5,28.5,35.5,42.5\text{ and }49.5$ .

Explanation of Solution

Given:

The gram of fats:

  $4,5,7,8,9,9,10,12,15,15,15,15,16,18,18,19,20,20,21,22,23,25,27,27,28,29,30,31,31,31,38,39,46,53$

Concept used:

Class marks are the mid value or mid-point of every interval.

  $\text{Class mark}=\frac{\text{upper limit}+\text{lower limit}}{2}.$

Calculation:

According to the given in Ascending order is:

  $4,5,7,8,9,9,10,12,15,15,15,15,16,18,18,19,20,20,21,22,23,25,27,27,28,29,30,31,31,31,38,39,46,53$

Class marks are the mid value or mid-point of every interval.

Since, class limits are:

  $4,11,18,25,32,39,46\text{ and }53.$

  $\text{class mark}=\frac{\text{upper limit}+\text{lower limit}}{2}.$

For the first interval the class marks:

  $\text{class mark}=\frac{\text{11}+\text{4}}{2}=\frac{15}{2}=\mathrm{7.5.}$

Similarly, it can be used to find the class mark respective class intervals or add $7$ order by order.

  $7.5,14.5,21.5,28.5,35.5,42.5\text{ and }49.5$ .

Hence, class marks are $7.5,14.5,21.5,28.5,35.5,42.5\text{ and }49.5$ .

(e)

To determine

To construct: the frequency distribution table for the gram o fats given below.

Answer to Problem 10E

The frequency distribution table the frequency can be calculated and total frequency is $38$ .

Explanation of Solution

Given:

The gram of fats:

  $4,5,7,8,9,9,10,12,15,15,15,15,16,18,18,19,20,20,21,22,23,25,27,27,28,29,30,31,31,31,38,39,46,53$ .

Concept used:

The frequency distribution table consist of frequency and tally marks which can easily measure the range class limits class size by looking at their respective blocks.

Calculation:

According to the given in Ascending order is:

  $4,5,7,8,9,9,10,12,15,15,15,15,16,18,18,19,20,20,21,22,23,25,27,27,28,29,30,31,31,31,38,39,46,53$

(f)

To determine

To graph: the histogram from the grams of fats listed below.

Answer to Problem 10E

From histogram its more cleared to mention the maximum and minimum frequency through which range can be solved.

Explanation of Solution

Given:

The gram of fats:

  $4,5,7,8,9,9,10,12,15,15,15,15,16,18,18,19,20,20,21,22,23,25,27,27,28,29,30,31,31,31,38,39,46,53$

Concept used:

The histogram chart can be draw through Microsoft excel and this histogram chart can give so many information regarding the data.

The histogram is most commonly used graph to show frequency distributions

The purpose of histogram is to graphically summarize the distribution of a univariate data set.

Calculation:

According to the given in Ascending order is:

  $4,5,7,8,9,9,10,12,15,15,15,15,16,18,18,19,20,20,21,22,23,25,27,27,28,29,30,31,31,31,38,39,46,53$ .

The histogram chart for the

  

Hence, from histogram its more cleared to mention the maximum and minimum frequency through which range can be solved.

(g)

To determine

To find: the intervals that describe the most fat contained in sandwiches.

Answer to Problem 10E

  $25-32$ .

Explanation of Solution

Given:

The gram of fats:

  $4,5,7,8,9,9,10,12,15,15,15,15,16,18,18,19,20,20,21,22,23,25,27,27,28,29,30,31,31,31,38,39,46,53$

Concept used:

The histogram chart can be draw through Microsoft excel and this histogram chart can give so many information regarding the data.

The histogram is most commonly used graph to show frequency distributions

The purpose of histogram is to graphically summarize the distribution of a univariate data set.

Calculation:

According to the given in Ascending order is:

  $4,5,7,8,9,9,10,12,15,15,15,15,16,18,18,19,20,20,21,22,23,25,27,27,28,29,30,31,31,31,38,39,46,53$

From the help of histogram chart the largest frequency can be measured as:

  $25-32$ is the largest frequency from the all intervals.

Hence, interval is $25-32$ .