Answer to Question #229844 in Statistics and Probability for Gushex

Question

If the median mass of 5 people in a lift is 65kg and a 70kg man enters then:

i) The new median will be about 66kg is it true and why

Answer 1

At first we have mass of 5 people

$$m_1\leq m_2\leq65\leq m_4\leq m_5$$

Now a 70kg man enters

If $m_4\geq70,$ we have

$$m_1\leq m_2\leq65<70\leq m_4\leq m_5$$

$$median_{new}=\dfrac{65+70}{2}=67.5$$

If $65\leq m_4\leq70,$ we have

$$m_1\leq m_2\leq65\leq m_4\leq 70\leq m_5$$

$$median_{new}=\dfrac{65+m_4}{2}$$

$$65\leq median_{new}\leq67.5$$

Depending on value $m_4$ the new median will be

$$65\leq median_{new}\leq67.5$$

I think that the statement is False.