Question

If the median of 10 observations 20, 22, 27, 28, 32, x+ 2, 39, 40, 41, 50 arranged in the ascending order is 34, then the value of x is

• A. 32
• B. 34
• C. 35
• D. 36

Answer 1

The Correct Option is B

\[ 20, 22, 27, 28, 32, x + 2, 39, 40, 41, 50. \]

Step 1: Recall the formula for the median.

The median is the middle value of a data set when the number of observations is odd, or the average of the two middle values when the number of observations is even. Here, there are 10 observations (even), so the median is the average of the 5th and 6th values.

Step 2: Identify the 5th and 6th values in the data set.

From the given data set, the 5th value is \( 32 \), and the 6th value is \( x + 2 \).

The median is given as 34. Therefore:

\[ \text{Median} = \frac{\text{5th value} + \text{6th value}}{2}. \]

Substitute the known values:

\[ 34 = \frac{32 + (x + 2)}{2}. \]

Step 3: Solve for \( x \).

Multiply through by 2 to eliminate the fraction:

\[ 68 = 32 + x + 2. \]

Simplify:

\[ 68 = 34 + x. \]

Solve for \( x \):

\[ x = 68 - 34 = 34. \]

Final Answer: The value of \( x \) is \( \mathbf{34} \), which corresponds to option \( \mathbf{(2)} \).