Chapter 10.1, Problem 12PPS

a.

To determine

To calculate the percentile of the tallest person in class.

Answer to Problem 12PPS

The tallest person is at 90^th percentile

Explanation of Solution

Given information:

The heights of students

Formula Used: Percentile formula is,

  $percentile=\frac{NumberOfValuesBeforeX}{n}\times 100$ ,

Where, n is the total number of item

Calculation:

Arranging the value of students in increasing order of their height,

Student	Height(inches)
G	58
AN	59
R	59
CA	60
CH	61
J	62
P	63
E	63
ANT	64
B	65

From the table it can be concluded that B is the tallest student and he is at 10^th position

Substituting the values in percentile formula,

  $percentile=\frac{9}{10}\times 100$

On solving,

  $Percentile=90$

Hence, the tallest person is at 90^th percentile.

Conclusion: The tallest person is at 90^th percentile

b.

To determine

To calculate the third shortest person’s percentile.

Answer to Problem 12PPS

The third shortest student is at 30^th percentile.

Explanation of Solution

Given information:

Height of students,

Student	Height(inches)
G	58
AN	59
R	59
CA	60
CH	61
J	62
P	63
E	63
ANT	64
B	65

Concept Used:

  $percentile=\frac{NumberOfValuesBeforeX}{n}\times 100$

Calculation:

From the table, Third shortest student is CA.

Substituting the values in percentile formula,

  $percentile=\frac{3}{10}\times 100$

On solving,

  $Percentile=30$

Hence, the third shortest student is at 30^th percentile.

Conclusion:

The third shortest person is at 30^th percentile.

c.

To determine

To calculate, if there is 50^th percentile

Answer to Problem 12PPS

There is no 50^th percentile in the given data.

Explanation of Solution

Given information: Height of students,

Student	Height(inches)
G	58
AN	59
R	59
CA	60
CH	61
J	62
P	63
E	63
ANT	64
B	65

Formula Used:

  $ValueOfX=\frac{percentile}{100}\times (n+1)$

Calculation:

Substituting the values,

  $X=\frac{50}{100}\times (10+1)$

So,

  $X=\frac{50}{100}\times 11$

On solving,

  $X=5.5$

In this situation, average of 5^th and 6^th term is to be calculated. Hence, substituting the values of 5^th and 6^th term,

  $=\frac{61+62}{2}$

On solving,

  $=61.5$

Comparing the value to the table,

Since, there is no student with 61.5 inches height. So, there is no 50^th percentile.

Conclusion: There is no 50^th percentile in the given data

d.

To determine

To calculate, if there is someone at 100^th percentile

Answer to Problem 12PPS

There is no value present on the 100^th percentile.

Explanation of Solution

Given information: Height of students,

Student	Height(inches)
G	58
AN	59
R	59
CA	60
CH	61
J	62
P	63
E	63
ANT	64
B	65

Formula Used:

  $ValueOfX=\frac{percentile}{100}\times (n+1)$

Calculation:

Substituting the values,

  $X=\frac{100}{100}\times (10+1)$

So,

  $X=\frac{100}{100}\times 11$

On solving,

  $X=11$

On comparing the value of X to the given table. Since, there are only 10 terms in the data.

There is no value present on the 100^th percentile.

Conclusion: There is no value present on the 100^th percentile.