Final answer:
To determine the set with the largest variance, one must calculate the average of the squared deviations from the mean for each set. After calculation, set 2 (-1, 3, 4, 7) has the largest variance of 8.1875.
Step-by-step explanation:
The question asks which set of numbers has the largest variance. To determine this, we calculate the variance for each set by following the necessary steps: find the mean of the set, subtract the mean from each number to find the deviation of each number, square each deviation, find the average of these squared deviations (which is the variance). Here are the calculations for each set:
- For set 1 (7, 8, 9, 10), the mean is 8.5. The deviations are -1.5, -0.5, 0.5, 1.5. Squaring these gives 2.25, 0.25, 0.25, 2.25. The average of these is 1.25.
- For set 2 (-1, 3, 4, 7), the mean is 3.25. The deviations are -4.25, -0.25, 0.75, 3.75. Squaring these gives 18.0625, 0.0625, 0.5625, 14.0625. The average of these is 8.1875.
- For set 3 (-4, -2, -1, 0), the mean is -1.75. The deviations are -2.25, -0.25, 0.75, 1.75. Squaring these gives 5.0625, 0.0625, 0.5625, 3.0625. The average of these is 2.1875.
- For set 4 (-1, 0, 2, 4), the mean is 1.25. The deviations are -2.25, -1.25, 0.75, 2.75. Squaring these gives 5.0625, 1.5625, 0.5625, 7.5625. The average of these is 3.6875.
Based on the calculated variances, set 2 with a variance of 8.1875 has the largest variance.