The nih body mass index categories are

1) BMI calculation

Subject       A                                  B                                   C

Age            57                                 30                                 18

Gender       Male                             Male                             Male

heigth         70 in                             72 in                             68
                   70 * 2.54 = 177.8cm    72*2.54=182.88cm      68*2.54=172.72 cm

weight        165 lb                           190 lb                           185 lb
                  165/2.2046=74.8kg      190/2.2046=86.2kg     185/2.2046=83.9kg

BMI            74.8*10,000                  86.2*10,000                83.9*10,000
                  = 23.7      = 25.8    = 28.1
                     (177.8)^2                     (182.88)^2                  (172.72)^2

2) Weight status

Subject A: 18.5 ≤ 23.7 ≤ 24.9 => Considered Ideal

Subject B: 20.5 ≤ 25.8 ≤ 29.9 => Considered Overweight

Subject C: 20.5 ≤ 28.1 ≤ 29.9 => Considered Obese

Ideal weight range

Inequality

             w * 10,000                   18.5*h^2               24.9*h^2
 18.5 ≤ ≤ 24.9 =>  ≤ w ≤   
                 h^2                           10,000                   10,000

Subject A: h = 177.8 cm =>

18.5*(177.8)^2           24.9*(177.8)^2
≤ w ≤
     10,000                      10,000

          58.5 kg ≤ w ≤ 78.7

Subject B: h = 182.88 cm
            
18.5*(182.88)^2              24.9*(182.88)^2
    ≤ w ≤
     10,000                            10,000

          61.9 kg ≤ w ≤ 83.3

Subject C:

18.5*(172.72)^2           24.9*(172.72)^2
≤ w ≤
     10,000                         10,000

          55.2 kg ≤ w ≤ 74.3 kg

3) Is BMI an appropiate measure of health?

Pros:

* it is quick and easy to calculate, so it provides a prompt measure.

Cons:

* It is not accurate.

* It leaves out specific conditions of the person: genetic and fitness.

I like that it provides a standardization to compare the status of different persons based on an objective measure, but you need to include other factors: age, gender, build, fat %, activities performed, among others. So, I am in favor of using it only like a factor but you need to use other additional measures.