Question

PRINTER VERSIO" ACK mm NT RESOURCES pter 03 Quiz .2 Question 9 The following data give the weights (in pounds) lost by 15 members of a health club at the end of 2 months after joining the club 4 23 9 19 12 4 9 12 17 646 17 14 13 a. Compute the values of the three quartiles and the interquartile range. ts by Study QR- b. Calculate the approximate value of the 82d percentile. Enter an exact value. c. Find the percentile rank of 12. Round your answer to the nearest integer SAVE FOR LATER SUBMIT ANSWE Question Attempts: 0 of 3 used

Answer 1

(a)

(i)

Q1 = 6

EXPLANATION:

Step 1:

Arranging numbers in ascending order, we get:

4,4,6,6,9,9,12,12,13,14,17,17,19,23

Step 2:

Take the lower half of the ascending set:

4,4,6,6,9,9

Middle value = 6.

So,

Q1 = 6

(ii)

Q2 = 12

EXPLANATION:

Step 1:

Arranging numbers in ascending order, we get:

4,4,6,6,9,9,12,12,13,14,17,17,19,23

Step 2:

Middle value = 12

So,

Q2 = 12

(iii)

Q3 = 17

EXPLANATION:

Step 1:

Arranging numbers in ascending order, we get:

4,4,6,6,9,9,12,12,13,14,17,17,19,23

Step 2:

Take the upper half of the ascending set:

12,13,14,17,17,19,23

Middle value = 17

So,

Q3 = 17

(iv)

IQR = 11

EXPLANATION:

IQR = Q3 - Q1 = 17 - 6 = 11

So,

IQR = 11

(b)

82nd percentile:

Arranging numbers in ascending order:

4,4,6,6,9,9,12,12,13,14,17,17,19,23

n = 15

Index i is given by:

$i = \frac{p}{100}\times n=\frac{82}{100}\times 15=12.3$

Since index i is not an integer, round up i = 13

The percentile is at the position i = 13.

It is: 17

So,

82nd percentile = 17

(c)

Percentile rank of 12:

n = 15

Arranging numbers in ascending order:

4,4,6,6,9,9,12,12,13,14,17,17,19,23

Number of values less than 12 is given by k = 7.

So,

Percentile rank of 12 is given by:

$\frac{k}{n}=\frac{7}{15}=0.4667$

               = 46.67 %