Answer:
Variance is 5.2575
Range is 7.6
Arithmetic Mean is 13.85
Step-by-step explanation:
Given the sample:
10.6, 12.6, 14.8, 18.2, 12.0, 14.8, 12.2, and 15.6.
(A) To calculate Variance
- Find the mean of the numbers, let the mean be M = (Sum of samples)/(number of samples)
M = (10.6 + 12.6 + 14.8 + 18.2 + 12.0 + 14.8 + 12.2 + 15.6)/8
= 110.8/8
= 13.85
- Subtract M from each sample, and square the result.
(10.6 - 13.85)² = 10.5625
(12.6 - 13.85)² = 1.5625
(14.8 - 13.85)² = 0.9025
(18.2 - 13.85)² = 18.9225
(12.0 - 13.85)² = 3.4225
(14.8 - 13.85)² = 0.9025
(12.2 - 13.85)² = 2.7225
(15.6 - 13.85)² = 3.0625
- Finally, variance is
V = (10.5625 + 1.5625 + 0.9025 + 18.9225 + 3.4225 + 0.9025 + 2.7225 + 3.0625)/8
= 42.06/8
= 5.2575
(B) Range = (Highest number in the sample) - (lowest number in the sample)
R = 18.2 - 10.6
= 7.6
(C) Arithmetic mean is M, which we have obtained earlier in (A)
M = 13.85