The daily sales of a small shop (in number of items) over 10 days were 13, 5, 22, 17, 9, 30, 26, 11, 4, 19. Find the median.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 15
Arrange the values in order. With 10 values (an even number), the median is the average of the 5th and 6th values.
In ascending order: 4, 5, 9, 11, 13, 17, 19, 22, 26, 30
The two middle values are 13 and 17
Median \(\displaystyle =\frac{13+17}{2}=15\)
The median is 15.
Why the other options are incorrect
Option (1) 17 — 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.
Option (2) 19.5 — Incorrect. This averages the two middle values of the list as written; the values must first be put in order.
Option (4) 13 — Incorrect. This is only the 5th value in order; the median of an even number of values is the average of the two middle ones.