If the variance of the data 2, 4, 5, 6, 17 is v, then what is the variance of the data 4, 8, 10, 12, 34?

Options

A. `v`
B. `4v`
C. `v^(2)`
D. `2v`

Explanation

To find the variance of the data set \(4, 8, 10, 12, 34\) in terms of the variance \(v\) of the data set \(2, 4, 5, 6, 17\), we can follow these steps:

### Step 1: Understand the relationship between the two data sets
The second data set \(4, 8, 10, 12, 34\) can be derived from the first data set \(2, 4, 5, 6, 17\) by multiplying each element of the first data set by 2.

### Step 2: Recall the property of variance
The variance of a data set changes when each element is multiplied by a constant \(K\). Specifically, if each element of a data set is multiplied by \(K\), the variance of the new data set is given by:
\[ \text{Variance of new data set} = K^2 \times \text{Variance of original data set} \]

### Step 3: Identify the constant \(K\)
In this case, \(K = 2\) since each element of the first data set is multiplied by 2 to obtain the second data set.

### Step 4: Calculate the variance of the new data set
Using the property of variance:
\[ \text{Variance of } (4, 8, 10, 12, 34) = K^2 \times v = 2^2 \times v = 4v \]

### Conclusion
Thus, the variance of the data set \(4, 8, 10, 12, 34\) is \(4v\).

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