Find the median of the data 40, 50, 30, 20, 80, 70, 90, 50. Next, if 30 is replaced by 120, find the new median.
The mean of the two medians found is _______

Correct option is A

Given:

Original data set is 40, 50, 30, 20, 80, 70, 90, 50.

Then 30 is replaced by 120.

Formula Used:

Median for an even number of observations

= $$(\frac{\text{Value at (n/2) position + Value at ((n/2)+1) position}} 2.$$​

Solution:

Original Set: 40, 50, 30, 20, 80, 70, 90, 50 Ordered Set: 20, 30, 40, 50, 50, 70, 80, 90

=> Median = $$\frac{(50 + 50)} 2 = \frac{100} 2$$​

=> Median = 50 After Replacing 30 with 120: New Set: 20, 40, 50, 50, 70, 80, 90, 120

=> New Median = $$\frac{(50 + 70)} 2 = \frac{120} 2$$​

=> New Median = 60

Mean of Two Medians: = Mean = $$\frac{(50 + 60)} 2 = \frac{110} 2$$​

=> Mean = 55