Chapter 14.1, Problem 11E

(a)

To determine

To find: The range of the first eighteen winter Olympic games.

Answer to Problem 11E

The range is $56$ .

Explanation of Solution

Given:

The number of nations:

  $16,17,25,28,28,30,30,32,35,36,37,37,37,49,57,64,67,72$

Concept used:

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

Calculation:

According to the given in Ascending order is:

  $16,17,25,28,28,30,30,32,35,36,37,37,37,49,57,64,67,72$ .

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

  $\begin{array}{l}\text{Range=highest value-lowest value}\text{.}\\ \text{Range=72}-16=56.\end{array}$

Hence, the range is $56$ .

(b)

To determine

To find: the appropriate class intervals of first eighteen winter Olympic games.

Answer to Problem 11E

Class interval is $8$ .

Explanation of Solution

Given:

The number of nations:

  $16,17,25,28,28,30,30,32,35,36,37,37,37,49,57,64,67,72$ .

Concept used:

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

Calculation:

According to the given in Ascending order is:

  $16,17,25,28,28,30,30,32,35,36,37,37,37,49,57,64,67,72$ .

Class interval can be found by:

  $\begin{array}{l}\text{Class interval=}\frac{\text{range}}{\text{divisibe of range}}.\\ \text{Class interval}=\frac{56}{7}=8.\end{array}$

Hence, class interval is $8$ .

(c)

To determine

To find: the class limit of a first eighteen winter Olympic games.

Answer to Problem 11E

Class limits are $16,24,32,40,48,56,64\text{ and 72}.$

Explanation of Solution

Given:

The number of nations:

  $16,17,25,28,28,30,30,32,35,36,37,37,37,49,57,64,67,72$ .

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:

  $16,17,25,28,28,30,30,32,35,36,37,37,37,49,57,64,67,72$ .

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

  $8$ and initial value is $16$ therefore the class limits are:

  $\begin{array}{l}16,16+8,16+16,16+24,16+32,+16+40,16+48,16+56.\\ 16,24,32,40,48,56,64\text{ and 72}.\end{array}$

Hence, the class limits are $16,24,32,40,48,56,64\text{ and 72}.$

(d)

To determine

To find: The class marks of first eighteen winter Olympic games.

Answer to Problem 11E

Class marks are $20,28,36,44,52,60\text{ and 68}$ .

Explanation of Solution

Given:

The number of nations:

  $16,17,25,28,28,30,30,32,35,36,37,37,37,49,57,64,67,72$ .

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:

  $16,17,25,28,28,30,30,32,35,36,37,37,37,49,57,64,67,72$ .

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

Since, class limits are:

  $16,24,32,40,48,56,64\text{ and 72}.$

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

For the first interval the class marks:

  $\text{class mark}=\frac{24+16}{2}=\frac{40}{2}=20$ .

Similarly, it can be used to find the class mark respective class intervals or add $8$ order by order.

  $20,28,36,44,52,60\text{ and 68}$ .

Hence, class marks are $20,28,36,44,52,60\text{ and 68}$ .

(e)

To determine

To construct: the frequency distribution table for the first eighteen winter Olympic games.

Answer to Problem 11E

From the frequency distribution tables the frequency can be calculated and total frequency is $18$ .

Explanation of Solution

Given:

The number of nations:

  $16,17,25,28,28,30,30,32,35,36,37,37,37,49,57,64,67,72$ .

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:

  $16,17,25,28,28,30,30,32,35,36,37,37,37,49,57,64,67,72$ .

(f)

To determine

To graph: the histogram from the first eighteen winter Olympic games.

Answer to Problem 11E

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

Explanation of Solution

Given:

The number of nations:

  $16,17,25,28,28,30,30,32,35,36,37,37,37,49,57,64,67,72$ .

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:

  $16,17,25,28,28,30,30,32,35,36,37,37,37,49,57,64,67,72$ .

The histogram chart:

  

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