Question

 An empirical relation between standard deviation (S.D), mean deviation about mean (M.D) and quartile deviation(Q.D) is
a)6 S.D = 5 M. D = 4 S.D
b)4 S.D = 5 M.D = 6 Q.D
c)5 S.D = 4 M.D = 6 Q.D
d)4 S.D = 6 M.D = 5 Q.D​

Answer 1

Given that,

An empirical relation between standard deviation, mean deviation and quartile deviation.

We know that,

The relation between standard deviation, mean deviation and quartile deviation.

$Q.D=\dfrac{2}{3}S.D$...(I)

$M.D\dfrac{4}{5}=S.D$....(II)

$Q.D=\dfrac{5}{6}M.D$....(III)

We need to find correct relation

Using given data

(a). S.D = 6

M.D= 5

Q.D = 4

For Q.D value,

Put the value in equation (I)

$Q.D=\dfrac{2}{3}\times6$

$Q.D=4$

For M.D value,

Now, put the value in equation (II)

$M.D\dfrac{4}{5}=S.D$

$M.D=\dfrac{5}{4}\times4$

$M.D = 5$

(a) is correct relation

(b). S.D = 4

M.D= 5

Q.D = 6

For Q.D value,

Put the value in equation (I)

$Q.D=\dfrac{2}{3}\times4$

$Q.D=\dfrac{8}{3}$

(b) is not correct relation.

(c). S.D = 5

M.D= 4

Q.D = 6

For Q.D value,

Put the value in equation (I)

$Q.D=\dfrac{2}{3}\times5$

$Q.D=\dfrac{10}{3}$

(c) is not correct relation.

(d). S.D = 4

M.D= 6

Q.D = 5

For Q.D value,

Put the value in equation (I)

$Q.D=\dfrac{2}{3}\times4$

$Q.D=\dfrac{8}{3}$

(d) is not correct relation.

Hence, (a). is correct option.

Answer 2

Ans:-

If s.d.=2 than q.d.=2/3 s.d.

=2/3×2 =4/3=1.333...

Than m.d.=4/5 s.d.

=4/5×2=8/5 = 1.6

The above example we can said that S.D.>M.D.>Q. D.