Question

The numbers 42, 43, 44, 44, (2x + 3), 45, 45, 46, 47 have been put in the ascending order. If the median is 45, find x. Hence, find the mode of the above data.

Answer 1

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.