Question

Thirteen internists in the Midwest are randomly selected, and each internist is asked to report last year’s income. The incomes obtained are

229,000 184,000 141,000 140,000 247,000
215,000 157,000 167,000 139,000 176,000
117,000 221,000 169,000

(a) Find the 90th percentile.

90th percentile         $

(b) Find the median.

Median          $

(c) Find the first quartile.

First quartile          $

(d) Find the third quartile.

Third quartile      $

(e) Find the 10th percentile.

10th percentile         $

(f) Find the interquartile range.

Interquartile range       $

(g-1) Develop a five-number summary.

	Income
Minimum	$
1st quartile	$
Median	$
3rd quartile	$
Maximum	$

(g-2) Choose a box plot of this data.

Answer 1

a)   Using Excel function percentile      
   90th percentile = percentile(data, 0.9)      
   90th percentile = $ 227,400      
          
b)   Using Excel function median      
   Median = median(data)      
   Median = $ 169,000      
          
c)   First Quartile is the 25th percentile      
   Using Excel function percentile       
   First quartile = percentile(data, 0.25)      
   First quartile = $ 141,000      
          
d)   Third Quartile is the 75th percentile      
   Using Excel function percentile       
   Third quartile = percentile(data, 0.75)      
   Third quartile = $ 215,000     
          
e)   Using Excel function percentile      
   10th percentile = percentile(data, 0.1)      
   10th percentile = $ 139,200     
          
f)   Interquartile range = Third Quartile - First Quartile      
       = 215000 - 141000      
       = 74000      
   Interquartile range = $ 74,000      
          
g-1)   Using Excel function min and max we get      
   Minimum = min(data)      
                = $ 117,000      
   Maximum = max(data)      
                = $ 247,000      
   From all above calculations, the five-number summary is       

g-2) Box plot

Note to student : Since you have not provided the options, you may choose the option closest   
to the boxplot given below  

Horizontal Box Plot

OR

Vertical Box plot