Let x be the median of data: 33, 42, 28, 49, 32, 37, 52, 57, 35, 41.
If 32 is replaced by 36 and 41 by 63, then the median of the data, so obtained, is y. What is the value of (x + y)?
Answer & explanation
Correct answer: option 2
Arrange the data in ascending order 28, 32, 33, 35, 37, 41, 42, 49, 52, 57
If n = 10 (even)
Median = \(\frac{(5^th + 6^th)}{2}\) = \(\frac{(37 + 41)}{2}\) = 39
⇒ x = 39
If 32 is replaced by 36 and 41 by 63, then
The new data is 33, 42, 28, 49, 36, 37, 52, 57, 35, 63
Arrange the data in ascending order 28, 33, 35, 36, 37, 42, 49, 52, 57, 63
If n = 10 (even)
Median = = \(\frac{(5^th + 6^th)}{2}\) = \(\frac{(37 + 42)}{2}\) = 39.5
⇒ y = 39.5
⇒ x + y
⇒ 39 + 39.5
⇒ 78.5