The following is a stem and leaf display of n 40 solar inte

The following is a stem and leaf display of n = 40 solar intensity measurements (integers in watts/m^2) on different days at a location in southern Australia. The (optional) first column of the stem and leaf plot contains a leaf count in a cumulative fashion from the top down to the stem that contains the median and also from the bottom up to the stem that contains the median. The stem containing the median has its own leaf count, shown in parentheses. Thus, 18 + 4 + 18 equals the sample size. Obtain the sample median and the 25th and the 75th percentiles. Obtain the sample interquartile range. What sample percentile is the 19th ordered value?

Solution

a) n =40 is even number

n/2=40/2=20

median = average of 20th and 21th value

20th value =717 21th value=717

= (717*-+717)/2 =717

n/4=10

25 th percentile = average of 10th and 11th value

=(691+699)/2=695

3n/4=30

75 th percentile = average of 30th and 31th value

=(734+734)/2 =734

b) IQR=Q3-Q1

Q3=734

Q1=695

IQR= 734-695= 39

c).19*100/40 =47.5

19th ordered value is 47.5 percentile.