Suppose the modified quota is 9.27. Fill in the blanks, and round your answers to two decimal places.
(a) Find the lower quota.
(b) Find the upper quota.
(c) Find the arithmetic mean of the lower and upper quotas.
(d) Find the geometric mean of the lower and upper quotas.
(e) Round the given modified quota by comparing it with the arithmetic mean.
(f) Round the given modified quota by comparing it with the geometric mean.
To answer these questions, we will break them down step by step.
(a) To find the lower quota, we will round down the modified quota to the nearest whole number. In this case, rounding down 9.27 gives us the lower quota of 9.
(b) To find the upper quota, we will round up the modified quota to the nearest whole number. Rounding up 9.27 gives us the upper quota of 10.
(c) To find the arithmetic mean of the lower and upper quotas, we add them together and divide by 2. In this case, (9 + 10) / 2 = 9.5.
(d) To find the geometric mean of the lower and upper quotas, we multiply them together and take the square root. In this case, √(9 * 10) = √90 ≈ 9.49.
(e) To round the given modified quota by comparing it with the arithmetic mean, we compare the decimal part of the modified quota with 0.5. If it is less than 0.5, we round down, otherwise, we round up. In this case, 0.27 is less than 0.5, so rounding down gives us 9.
(f) To round the given modified quota by comparing it with the geometric mean, we compare the decimal part of the modified quota with 0.49. If it is less than 0.49, we round down, otherwise, we round up. In this case, 0.27 is less than 0.49, so rounding down gives us 9.
So, the answers are:
(a) Lower quota: 9
(b) Upper quota: 10
(c) Arithmetic mean: 9.5
(d) Geometric mean: 9.49
(e) Rounded modified quota (comparing with arithmetic mean): 9
(f) Rounded modified quota (comparing with geometric mean): 9