Question

The median of certain observations 17, 18, 23, 27 x – 3, x + 5, 45, 49, 74 and 85 arranged in an ascending order is 35. Later on, it was found that one observation 72 was misread as 27 by mistake. The correct median of the data is: 

1. 36 

2. 38 

3. 42 

4. 47

Answer 1

 3. 42

17, 18, 23, 27, x –3, x + 5, 45, 49, 74, 85

\(\frac{x-3+x+5}{2}=35\)

\(\frac{2x+2}{2}=35\)

x + 1 = 35

x = 34

∴ The number are 17, 18, 23, 31, 39, 45, 49, 72, 74, 85

∴ Median = \(\frac{39+45}{2}=\frac{84}{2}=42\)