Question

The weight of 60 boys are given in the following distribution table:

Weight (kg)	37	38	39	40	41
No. of boys	10	14	18	12	6

Find:

1. Median 
2. Lower quartile 
3. Upper quartile 
4. Inter-quartile range  

Answer 1

Weight (kg) x	No. of boys f	Cumulative frequency
37	10	10
38	14	24
39	18	42
40	12	54
41	6	60

Number of terms = 60 

i. Median = The mean of the 30^th and 31^st terms 

∴ Median = `(39 + 39)/2`

= `78/2`

= 39 

ii. Lower quartile (Q₁) = `60^(th)/4` term

= 15^th term

= 38 

iii. Upper quartile (Q₃) = `(3 xx 60^(th))/4` term

= 45^th term

= 40 

iv. Inter-quartile range = Q₃ – Q₁

= 40 – 38

= 2