Find the median of the data 42, 15, 38, 27, 61, 19, 33, 54, 8, 47, 25, 70.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 35.5
Arrange the values in order. With 12 values (an even number), the median is the average of the 6th and 7th values.
In ascending order: 8, 15, 19, 25, 27, 33, 38, 42, 47, 54, 61, 70
The two middle values are 33 and 38
Median \(\displaystyle =\frac{33+38}{2}=35.5\)
The median is 35.5.
Why the other options are incorrect
Option (1) 26 — Incorrect. This averages the two middle values of the list as written; the values must first be put in order.
Option (2) 38 — Incorrect. This is only the 7th value in order; the median of an even number of values is the average of the two middle ones.
Option (3) 33 — Incorrect. This is only the 6th value in order; the median of an even number of values is the average of the two middle ones.