The median of the data \(9,12,1,20,25,5,18,15,21,11\) is \(M_1\). If 10 is included in the data, then the median of the new data is \(M_2\). What is the value of \(\left(M_1-M_2\right)\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1.5
The median is the middle value of the data arranged in order. With an even number of values it is the mean of the two middle values; with an odd number it is the single middle value.
Ten values (even):
In order: 1, 5, 9, 11, 12, 15, 18, 20, 21, 25
The middle values are the 5th and 6th: \(\displaystyle M_1=\frac{12+15}{2}=13.5\)
With 10 included (eleven values, odd):
In order: 1, 5, 9, 10, 11, 12, 15, 18, 20, 21, 25
The middle value is the 6th: \(M_2=12\)
The difference:
\(M_1-M_2=13.5-12=1.5\)