Chapter 10.5, Problem 15PPS

To determine

To construct a histogram for each set of data.

Explanation of Solution

Given information: Given data is,

Graph:

For 1^st period

  

For 6^th period

  

Interpretation:

Both the graphs are unstable. Values are increasing and decreasing.

To determine

To compare the sets using 5 number summary.

Answer to Problem 15PPS

The five number summary for 1^st period is,

206,291,350.5,439,578

The five number summary for 6^th period is,

294,316,392,451,509

Explanation of Solution

Given information: Given data is,

Formula used: Median is,

  $M=\frac{{(\frac{n}{2})}^{th}+{(\frac{n}{2}+1)}^{th}}{2}term$

Lower quartile is,

  $Q1=(n+1)\frac{1}{4}$

Upper quartile is,

  $Q3=(n+1)\frac{3}{4}$

Calculation:

Re-arranging the data in an ascending order,

1st Period

206,227,253,258,267,283,291,297,303,311,325,331,343,358,372,388,413,427,438,439,456,484,482,506,511,578

6th Period

294,296,297,312,333,308,319,341,352,357,359,378,379,392,401,405,409,421,438,440,451,467,485,490,500,502,506

For 1^st period median,

Substituting the values,

  $M=\frac{{(\frac{26}{2})}^{th}+{(\frac{26}{2}+1)}^{th}}{2}$

On solving,

  $M=\frac{{13}^{th}+{14}^{th}}{2}term$

Substituting the values,

  $M=\frac{343+358}{2}$

On solving,

  $M=350.5$

Hence, Median is 350.5

For 6^th period median,

Substituting the values,

  $M=\frac{27+1^{th}}{2}term$

On solving,

  $M={14}^{th}term$

Substituting the values,

  $M=392$

Hence, Median is 392

For 1^st period lower quartile,

Substituting the values,

  $Q1=(26+1)\frac{1}{4}$

On solving,

  $Q1=6.75$

Rounding off,

  $\approx 7$

Substituting the value,

  $Q1=291$

Hence, 1^st period Lower quartile is 291

For 1^st period higher quartile,

Substituting the values,

  $Q3=(26+1)\frac{3}{4}$

On solving,

  $Q3=20.25$

Rounding off,

  $\approx 20$

Substituting the values,

  $Q3=439$

Hence, 1^st period higher quartile is 439

For 6^th period lower quartile,

Substituting the values,

  $Q1=(27+1)\frac{1}{4}$

On solving,

  $Q1=7$

Substituting the value,

  $Q1=319$

Hence, 6^th period Lower quartile is 319

For 6^th period higher quartile,

Substituting the values,

  $Q3=(27+1)\frac{3}{4}$

On solving,

  $Q3=21$

Substituting the value,

  $Q3=451$

Hence, 6^th period higher quartile is 451

For 1^st period

Minimum is the smallest value of dataset.

Hence, minimum is 206.

Maximum is the largest value of the dataset.

Hence, maximum is 578.

For 6^th period

Minimum is the smallest value of dataset.

Hence, minimum is 294.

Maximum is the largest value of the dataset.

Hence, maximum is 509.

The five number summary for 1^st period is,

206,291,350.5,439,578

The five number summary for 6^th period is,

294,316,392,451,509

Five number summary is used as it is less time consuming and more efficient.