The given observations in ascending order are
42, 43, 44, 44, (2x + 3), 45, 45, 46, 47
Here, number of observations is 9 which is odd. So there will be one median class i.e.\((\frac{n+1}{2})\)th term
Median = Value of \((\frac{n+1}{2})\)th term \((\frac{9+1}{2})\)th term = 5th term
⇒ Median = 2x + 3
But Median = 45 (given)
45 = 2x + 3
⇒ 2x = 42
⇒ x = 21
The observations are 42, 43, 44, 44, 45, 45, 45, 46, 47.
The number 45 occurs most frequently i.e. 3 times.
Hence, Mode of the above data is 45.
Hence, x = 21 and Mode = 45.