आंकड़ों `2 ,5 ,6 ,x ,4 ,3 ` का माध्य 5 है। अब यदि x के स्थान पर 16 कर लिया जाए तो माध्य कितना बढ़ जाएगा ?

Options

A. 0
B. 1
C. 2
D. 3

Answer

To solve the problem step by step, we need to find the mean of the given numbers and then determine how it changes when we replace \( x \) with 16.

### Step 1: Calculate the mean of the original set of numbers

The original numbers are \( 2, 5, 6, x, 4, 3 \) and we know that their mean is 5.

The formula for the mean is:

\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \]

Given that the mean is 5, we can set up the equation:

\[ 5 = \frac{2 + 5 + 6 + x + 4 + 3}{6} \]

### Step 2: Simplify the equation

First, calculate the sum of the known numbers:

\[ 2 + 5 + 6 + 4 + 3 = 20 \]

Now substitute this back into the equation:

\[ 5 = \frac{20 + x}{6} \]

### Step 3: Solve for \( x \)

Multiply both sides by 6 to eliminate the fraction:

\[ 30 = 20 + x \]

Now, subtract 20 from both sides:

\[ x = 30 - 20 = 10 \]

### Step 4: Replace \( x \) with 16 and calculate the new mean

Now we replace \( x \) with 16 in the set of numbers:

The new set of numbers is \( 2, 5, 6, 16, 4, 3 \).

Calculate the new sum:

\[ 2 + 5 + 6 + 16 + 4 + 3 = 36 \]

### Step 5: Calculate the new mean

Using the mean formula again:

\[ \text{New Mean} = \frac{36}{6} = 6 \]

### Step 6: Find the increase in mean

Now, we find the increase in mean:

\[ \text{Increase in Mean} = \text{New Mean} - \text{Old Mean} = 6 - 5 = 1 \]

### Final Answer

The mean increases by 1.

---