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, you will need to understand what the lower quota, upper quota, arithmetic mean, and geometric mean are.
The lower quota is the largest whole number less than or equal to the modified quota. To find it, you can simply round down the modified quota to the nearest whole number.
(a) The lower quota is 9.
The upper quota is the smallest whole number greater than or equal to the modified quota. To find it, you can round up the modified quota to the nearest whole number.
(b) The upper quota is 10.
The arithmetic mean is the average of two numbers. To find it, you add the lower and upper quotas and divide by 2.
(c) The arithmetic mean is (9 + 10) / 2 = 9.5.
The geometric mean is the square root of the product of two numbers. To find it, you multiply the lower and upper quotas and then take the square root.
(d) The geometric mean is √(9 * 10) = √90 ≈ 9.49.
To round the given modified quota by comparing it with the arithmetic mean, you compare which one it is closer to. If the modified quota is closer to the lower quota, you round down to the lower quota. If it is closer to the upper quota, you round up to the upper quota.
(e) Since the modified quota is 9.27 and it is closer to the lower quota (9) than the upper quota (10), you round down to the lower quota: 9.27 rounded to the nearest whole number is 9.
To round the given modified quota by comparing it with the geometric mean, you also compare which one it is closer to. If the modified quota is closer to the geometric mean, you round down to the lower quota. If it is closer to the arithmetic mean, you round up to the upper quota.
(f) Since the modified quota is 9.27 and it is closer to the geometric mean (9.49) than the arithmetic mean (9.5), you round down to the lower quota: 9.27 rounded to the nearest whole number is 9.
So, the answers are:
(a) Lower quota is 9.
(b) Upper quota is 10.
(c) Arithmetic mean is 9.5.
(d) Geometric mean is 9.49.
(e) Rounded modified quota by comparing with the arithmetic mean is 9.
(f) Rounded modified quota by comparing with the geometric mean is 9.