Mean of first 11 multiples of 11 is x and median of that numbers is y. Find x : y.

Answer

To solve the problem, we need to find the mean (x) and median (y) of the first 11 multiples of 11, and then calculate the ratio x : y.

### Step 1: List the first 11 multiples of 11
The first 11 multiples of 11 are:
- 11 × 1 = 11
- 11 × 2 = 22
- 11 × 3 = 33
- 11 × 4 = 44
- 11 × 5 = 55
- 11 × 6 = 66
- 11 × 7 = 77
- 11 × 8 = 88
- 11 × 9 = 99
- 11 × 10 = 110
- 11 × 11 = 121

Thus, the multiples are: **11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121**

### Step 2: Calculate the Mean (x)
To find the mean, we sum all the multiples and divide by the total number of multiples.

Sum of the multiples:
\[ 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99 + 110 + 121 \]

Calculating the sum:
\[ = 11 + 22 = 33 \\ = 33 + 33 = 66 \\ = 66 + 44 = 110 \\ = 110 + 55 = 165 \\ = 165 + 66 = 231 \\ = 231 + 77 = 308 \\ = 308 + 88 = 396 \\ = 396 + 99 = 495 \\ = 495 + 110 = 605 \\ = 605 + 121 = 726 \]

Now, divide the total by the number of multiples (11):
\[ \text{Mean} (x) = \frac{726}{11} = 66 \]

### Step 3: Calculate the Median (y)
To find the median, we need to identify the middle value in the ordered list of numbers. Since we have 11 numbers (an odd count), the median is the middle number.

The middle position is given by:
\[ \text{Median position} = \frac{n + 1}{2} = \frac{11 + 1}{2} = 6 \]

The 6th term in the list is:
**66**

Thus, the median (y) is:
\[ y = 66 \]

### Step 4: Calculate the ratio x : y
Now we have:
- Mean (x) = 66
- Median (y) = 66

To find the ratio:
\[ x : y = 66 : 66 = 1 : 1 \]

### Final Answer
The ratio \( x : y \) is \( 1 : 1 \).

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