Final answer:
The average of the replicated list is 4.2, and the standard deviation is approximately 2.41. The original average and standard deviation were changed due to the replication of the data points.
Step-by-step explanation:
The original data file contains the numbers 3, 5, 2, 7, and 8. However, due to a mistake, these numbers were replicated, resulting in a new list with 6 data points: 3, 5, 2, 7, 8, 3, 5, 2, 7, and 8. To find the average, add up all the numbers and divide by the total count. In this case, the sum is 42 (3+5+2+7+8+3+5+2+7+8) and the count is 10. So the average is 42/10 = 4.2.
To calculate the standard deviation, you need to calculate the variance first. Variance is calculated by finding the difference between each data point and the average, squaring the difference, summing all the squared differences, and dividing by the count. The variance is then the square root of the average of these squared differences.
Now, let's calculate the variance for the replicated list. The differences between each data point and the average are: (-1.2, 0.8, -2.2, 2.8, 3.8, -1.2, 0.8, -2.2, 2.8, 3.8). Squaring these differences, we get: (1.44, 0.64, 4.84, 7.84, 14.44, 1.44, 0.64, 4.84, 7.84, 14.44). Summing these squared differences, we get 58.12. Dividing by the count, we get the variance: 58.12/10 = 5.812.
Finally, taking the square root of the variance, we get the standard deviation: √(5.812) ≈ 2.41.