1.

Median of the data 6, 10, 20, x, 12, 14 is 12, then x =A) 6 B) 12C) 4 D) 14

Answer»

Correct option is: B) 12

Given that median of data 6, 10, 20, x, 12, 14 is 12.

(A) If x = 6,

then ascending order of observation is as follows :

6, 6, 1 0 > 12, 14, 20 total 6 observations

\(\therefore\) Median = \(\frac {\frac n2th(\frac n2 + 1)^{th}}{2} = \frac {3^{rd} + 4^{th}}{2} = \frac {10+12}{2} = \frac {22}2 = 11\)

(B) If x = 12

Then ascending order of observations is as follows :

6, 10, 12, 12, 14, 20

\(\therefore\) Median = \(\frac {12 + 12}{2} = \frac {24}2 =12\)

(C) If x = 4

Then ascending order of observation is as follows:

4, 6, 10, 12, 14, 20.

\(\therefore\) Median = \(\frac {10 + 12}{2} = \frac {22}2 =11\)

(D) If x = 14

Then ascending order of observation is as follows:

 6, 10, 12, 14, 14, 20.

\(\therefore\) Median = \(\frac {12 + 14}{2} = \frac {26}2 =13\)

Correct option is: B) 12


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