Question

The mean of the observations 29, x + 1, 33, 44, x + 3, x + 6 and 46 is 39. Then, the median of the observations is :

• A. 41.5
• B. 40
• C. 39.5
• D. 38

Answer 1

Answer:

B. 40

Solution:

Formula used : 

Average = Sum of all observations $\div$ Number of observations

Median =  $\frac{(n + 1)}{2}$

Calculation :

Average = $\frac{(29+x+1+33+44+x+3+x+6+46)}{7}=39$

⇒ 162 + 3x = 273 

⇒ 3x = 111

⇒ x = 37

Numbers are 29, 38, 33, 44, 40, 43, 46

After arranging in ascending order : 29, 33, 38, 40, 43, 44, 46

Median = $\frac{(7 + 1)}{2}$ = 4^th observation

Median = 40

∴ The correct answer is 40.