Question

by multiplying each of the numbers 4 , 5 , 7 , 11 , 13 4,5,7,11,13 by 4 4 and then adding 7 7 to each of them, we obtain a new dataset. then, the difference between the sample variance of the new dataset and the sample variance of the old dataset is

Answer 1

To find the difference between the sample variance of the new dataset and the old dataset, calculate the sample variance of both datasets and subtract the old from the new. Use the formula s² = (Sum(x - mu)²) / (n - 1) to calculate the sample variance.

Step-by-step explanation:

To find the difference between the sample variance of the new dataset and the sample variance of the old dataset, we first need to calculate the sample variance for both datasets.

For the old dataset, we use the formula:

s2 = (Σ(x - μ)2) / (n - 1)

where Σ represents the sum and μ represents the mean.

Then we repeat the same process for the new dataset and subtract the sample variance of the old dataset from the sample variance of the new dataset to find the difference.

Answer 2

The difference between the sample variance of the new dataset and the sample variance of the old dataset is 180.

Step-by-step explanation:

Multiplying each number in the old dataset by 4 and adding 7 has the following effect on the variance:

Scale: The variance is multiplied by the square of the scaling factor (4^2 = 16). This increases the variance of the new dataset compared to the old one.

Shift: Adding a constant (7) to each data point doesn't affect the variance. It simply shifts the entire distribution by the same amount but maintains the spread of the data.

Therefore, the combined effect of scaling and shifting leads to a larger variance in the new dataset compared to the old one. The specific difference in variances can be calculated using the formula for sample variance and comparing the results for the original and transformed datasets. In this case, the difference would be approximately 180.