Question

The numbers 42, 43, 44, 44, (2x+3), 45, 45, 46, 47 have been arranged in an ascending order and their median is 45. Find the value of x. Hence, find the mode of the above data.

Answer 1

ANSWER:
Arranging the given data in ascending order:
42, 43, 44, 44, (2x + 3), 45, 45, 46, 47
Number of terms = 9 (odd)
∴ Median=(n+1)/2th term
⇒45=(9+1)/2th term
⇒45=5th term⇒45=2x+3⇒2x=45-3⇒2x=42⇒x=21
Hence, the value of x is 21.
Arranging the given data in ascending order:
42, 43, 44, 44, 45, 45, 45, 46, 47
Here, 45 occurs maximum number of times.
∴ Mode = 45
Hence, the mode of the data is 45.