alkaser266,

Your formula seems to be the median of a r.v with a group frequency distribution. Below is an example:

The following frequency distribution table shows test scores earned

by a group of 671 trainees:

Scores Frequency

45-50 2

50-55 9

55-60 19

60-65 38

65-70 60

70-75 117

75-80 146

80-85 132

85-90 99

90-95 36

95-100 13

Total 671

Define:

L = Lower exact limit of the median class.

nb = Cumulative Frequency of the class preceding the median class

nm = Cumulative Frequency of the median class

i = the width of the median class.

N = the total.

median=L + i*(N/2 - nb)/nm

2+9+19+38+60+117+146=391

Hence the class 75-80 contains the median.

L=75

nb=2+9+19+38+60+117=245

nm=2+9+19+38+60+117+146=391

i=5

N=671

median=L+i*(N/2 - nb)/nm = 75+5*(671/2 - 245)/391

=76.16

The notation is different but it's the same formula.