Question

The numbers 52,53, 54, 54, (2x+1), 55, 55, 56,57 have been arranged in an ascending order and their median is 55. Find the value of x and hence find the mode of the given data.

Answer 1

ANSWER:
Arranging the given data in ascending order:
52, 53, 54, 54, (2x + 1), 55, 55, 56, 57
Number of terms = 9 (odd)
∴ Median=(n+1)/2th term⇒55=(9+1)/2th term⇒55=5th term
⇒55=2x+1
⇒2x=55-1⇒2x=54⇒x=27
Hence, the value of x is 27.
Arranging the given data in ascending order:
52, 53, 54, 54, 55, 55, 55, 56, 57Here, 55 occurs maximum number of times.
∴ Mode = 55
Hence, the mode of the data is 55.