Question

How to verify whether the Mode, Median , Mean which we got are correct or not???

Answer 1

$\bold{\large{\underline{Answer\: \colon}}}$

The expression is coined by a mathematician named as :

$\bold{\boxed{Karl\: Pearson}}$

If we know any two values in the given expression then we verify our answer.

$\bold{\boxed{\boxed{Mode \:= \: 3Median\: -\: 2Mean}}}$

General Formula's of 3M are

$\bold{\large{1)\:Mean \: = \: \overline{x} \: = \: \dfrac{\sum \: x}{N}}}$

$\overline{x} \: = \: mean \: of \: set$

$\sum \: x \: = \: sum\: of\: x \: value$

$N \: is \: the \: number \: of \: x \: value$

$\bold{\large{2) \: Median\: = \: l \:+ \: \dfrac{h}{f}\Bigg(\dfrac{N}{2}\: - \: c \Bigg) }}$

where,

l = lower class boundary of the median class

h = size of median class interval

f = frequency corresponding to median class

N = sum of the frequencies

c = cumulative frequency preceding median class

$\bold{\large{3)\: Mode \: = \: l \: + \: h \: \Bigg(\dfrac{f_{m} \: - \: f_{1}}{2f_{m} \: - \: f_{1} \: - \: f_{2}}\Bigg) }}$

l = Lower boundary of modal class

h = size of modal class

$f_{m}$ = Frequency corresponding to modal class

$f_{1}$ = Frequency preceding to modal class

$f_{2}$ = Frequency

proceeding modal class

These are some general formula and above one is empirical verification formula.

$\bold{\large{Thanks}}$