Question

Prove that for a normal distribution, the quartile deviation, the mean deviation and standard
deviation are in the ratio 10 : 12 : 15 approximately​

Answer 1

Given :- Prove that for a normal distribution, the quartile deviation, the mean deviation and standard deviation are in the ratio 10 : 12 : 15 approximately ?

Solution :-

for a normal distribution , the relation between standard deviation, mean deviation and quartile deviation is :-

• 4SD = 5MD
• 2SD = 3QD

so,

→ 4SD = 5MD

→ MD = (4/5)SD

and,

→ 2SD = 3QD

→ QD = (2/3)SD

then,

→ QD : MD : SD = (2/3)SD : (4/5)SD : SD

→ QD : MD : SD = (2/3) : (4/5) : 1

→ QD : MD : SD = (2*5 : 4*3 : 1*15)/15

→ QD : MD : SD = 10 : 12 : 15 (Ans.)

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Which relation among three measures of central tendency, mean, median and mode is correct? 

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