When you calculate a mean, the sign of the quotient always depend on the sign of the dividend. Why?

Mean = ∑x/n

When calculating a mean, which is essentially finding the average, the sign of the quotient does not always depend on the sign of the dividend. The sign of the quotient is determined by the signs of both the dividend and the divisor.

To understand this better, let's consider a few scenarios:

1. Positive dividend and positive divisor:
In this case, the quotient will be positive. For example, if you have 5 divided by 2, the quotient is 2.5, which is positive.

2. Negative dividend and positive divisor:
In this case, the quotient will be negative. For example, if you have -8 divided by 4, the quotient is -2, which is negative.

3. Positive dividend and negative divisor:
In this case, the quotient will be negative. For example, if you have 10 divided by -5, the quotient is -2, which is negative.

4. Negative dividend and negative divisor:
In this case, the quotient will be positive. For example, if you have -12 divided by -3, the quotient is 4, which is positive.

Therefore, the sign of the quotient depends on both the sign of the dividend and the divisor, not just the dividend alone.

When calculating the mean, also known as the average, of a set of numbers, the sign of the quotient depends on the signs of the individual numbers being averaged. This is because the sign indicates the direction or nature of the value and combining numbers with different signs can have different effects on the result.

To understand why the sign of the quotient depends on the sign of the dividend (the number being divided), we need to consider the two possible cases: positive dividends and negative dividends.

1. Positive Dividends:
When a dividend is positive, it means that the number being divided is greater than zero. In this case, the sign of the quotient will be determined by the signs of other numbers involved in the calculation.

- If all the numbers being averaged are positive, the quotient will also be positive because positive numbers divided by positive numbers result in a positive quotient.
- If one or more of the numbers being averaged are negative, the quotient will still be positive. This is because dividing by positive numbers reduces the magnitude of the negative numbers, making them closer to zero and resulting in a positive quotient.

2. Negative Dividends:
When a dividend is negative, it means that the number being divided is less than zero. This scenario results in different outcomes compared to positive dividends.

- If all the numbers being averaged are negative, the quotient will also be negative because negative numbers divided by negative numbers result in a positive quotient.
- If one or more of the numbers being averaged are positive, the quotient will be negative. This is because dividing positive numbers by negative numbers flips their sign and generates a negative quotient.

In summary, the sign of the quotient when calculating the mean depends on the signs of the individual numbers being averaged.