The mean of the following numbers is 68. Find the value of 'x'.
45, 52, 60, x, 69, 70, 26, 81 and 94.
Hence, estimate the median.

Answer

To solve the problem step by step, we need to find the value of 'x' given that the mean of the numbers is 68. Then, we will estimate the median of the numbers including 'x'.

### Step 1: Write down the formula for the mean.
The mean (average) is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of all observations}}{\text{Total number of observations}} \]

### Step 2: Set up the equation using the given mean.
We know the mean is 68 and there are 9 observations (including 'x'):
\[ 68 = \frac{45 + 52 + 60 + x + 69 + 70 + 26 + 81 + 94}{9} \]

### Step 3: Multiply both sides by 9 to eliminate the denominator.
\[ 68 \times 9 = 45 + 52 + 60 + x + 69 + 70 + 26 + 81 + 94 \]
\[ 612 = 45 + 52 + 60 + x + 69 + 70 + 26 + 81 + 94 \]

### Step 4: Calculate the sum of the known numbers.
Now, let's add the known numbers:
\[ 45 + 52 + 60 + 69 + 70 + 26 + 81 + 94 = 497 \]

### Step 5: Substitute the sum back into the equation.
Now we can substitute this sum back into the equation:
\[ 612 = 497 + x \]

### Step 6: Solve for 'x'.
To find 'x', subtract 497 from both sides:
\[ x = 612 - 497 \]
\[ x = 115 \]

### Step 7: List all numbers including 'x'.
Now that we have found 'x', the numbers are:
\[ 45, 52, 60, 115, 69, 70, 26, 81, 94 \]

### Step 8: Arrange the numbers in ascending order.
Arranging these numbers in ascending order gives:
\[ 26, 45, 52, 60, 69, 70, 81, 94, 115 \]

### Step 9: Find the median.
Since there are 9 observations (an odd number), the median is the middle number:
\[ \text{Median} = \text{5th term} = 69 \]

### Final Answers:
- The value of 'x' is **115**.
- The median is **69**.

---