If you add the same constant to each element of a sample then the mean of this collection of values will be the mean of the original sample plus the constant.
If you multiply each element of a sample by a constant then the mean of this collection of values will be the mean of the original sample multiplied by the constant.
When adding and subtracting a constant amount means that that amount will increase. The amount will increase dew to adding each number.
Since each event is independent (heads in one coin does not affect the probability of the other two coin flips), the multiplication rule applies: 1/2 x 1/2 x 1/2 = 1/8 or 0.125. So we can say the probability is 12.5%.
The gender of children is not a constant. It depends on the parental predispositions - mainly on the father's genes but apparently the mother's age can also affect the gender. The details of these influences are not understood well enough to develop an accurate model. If you make the simplistic but unjustified assumption that both genders are equally likely, the answer is 1/8.
An outlier can increase or decrease the mean and median It usually doesn't affect the mode
No. Outliers are part of the data and do not affect them. They will, however, affect statistics based on the data and inferences based on the data.
The grouping property, also known as the associative property, states that the way in which numbers are grouped in an arithmetic operation (addition or multiplication) does not affect the result. For addition, (a + b) + c = a + (b + c). For multiplication, (a * b) * c = a * (b * c).
The associative property of addition and multiplication both state that the grouping of numbers does not affect the result of the operation. In addition, changing the grouping of addends (e.g., (a + b) + c = a + (b + c)) yields the same sum, while in multiplication, changing the grouping of factors (e.g., (a × b) × c = a × (b × c)) results in the same product. Both properties emphasize the importance of the operations' structure over the specific numbers involved, allowing for flexibility in computation. Thus, they highlight the consistency and predictability of arithmetic operations.
The order in which the addends (in addition) or multiplicands (in multiplication) does not affect the answer. If symbolic form: a + b = b + a or a * b = b * a
Assuming you mean definition, commutative is a property of an operation such that the order of the operands does not affect the result. Thus for addition, A + B = B + A. Multiplication of numbers is also commutative but multiplication of matrices is not. Subtraction and division are not commutative.
An inverse operation undoes the effect of another operation. For example, addition is the inverse operation of subtraction, and multiplication is the inverse operation of division. Applying an operation and its inverse leaves you with the original value.
It is the property of operations such as addition or multiplication which state that the order in which the operations are carried out does not affect the result. That is, (A + B) + C = A + (B + C) and so, without ambiguity, you can write these as A + B + C.
Commutative Property of Multiplication
The commutative property states that changing the order of operands in a binary operation does not affect the result. More simply, and using more familiar terms: for addition, it means that A + B = B + A or for multiplication, A * B = B *A Subtraction and division are not commutative, nor is matrix multiplication.
The property you are referring to is the Associative Property. This property applies to both addition and multiplication, stating that when you add or multiply numbers, the way in which the numbers are grouped does not affect the final result. For example, in addition, ( (a + b) + c = a + (b + c) ), and in multiplication, ( (a \times b) \times c = a \times (b \times c) ).
The commutative property refers to a fundamental property of certain operations in mathematics, specifically addition and multiplication. It states that the order in which two numbers are combined does not affect the result; for example, (a + b = b + a) for addition, and (a \times b = b \times a) for multiplication. This property holds true for real numbers, integers, and many other mathematical structures. However, it does not apply to operations like subtraction or division.
The commutative property in mathematics states that the order in which two numbers are added or multiplied does not affect the result. For addition, this property is represented as a + b = b + a. For multiplication, it is represented as a x b = b x a.
The force constant is unaffected; It is a constant.