If the variance of 14, 18, 22, 26, 30 is 'k", then find the variance of 28, 36, 44, 52, 60.

Answer

To find the variance of the numbers 28, 36, 44, 52, and 60, given that the variance of 14, 18, 22, 26, and 30 is \( k \), we can follow these steps:

### Step 1: Understand the relationship between the two sets of numbers
The numbers 28, 36, 44, 52, and 60 can be expressed as multiples of the numbers 14, 18, 22, 26, and 30:
- \( 28 = 2 \times 14 \)
- \( 36 = 2 \times 18 \)
- \( 44 = 2 \times 22 \)
- \( 52 = 2 \times 26 \)
- \( 60 = 2 \times 30 \)

### Step 2: Identify the scaling factor
From the above expressions, we can see that each number in the second set is obtained by multiplying each corresponding number in the first set by 2. Thus, the scaling factor \( m \) is 2.

### Step 3: Use the property of variance under scaling
The property of variance states that if you multiply all observations by a constant \( m \), the variance of the new set of observations is given by:
\[ \text{Variance(new)} = m^2 \times \text{Variance(original)} \]
In this case, since the variance of the original set (14, 18, 22, 26, 30) is \( k \), we can write:
\[ \text{Variance(28, 36, 44, 52, 60)} = 2^2 \times k = 4k \]

### Step 4: Conclusion
Thus, the variance of the numbers 28, 36, 44, 52, and 60 is \( 4k \).

### Final Answer:
The variance of 28, 36, 44, 52, and 60 is \( 4k \).

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