Answer:
Mean = 3.12, Variance = 3.324, Standard deviation = 1.8232
Step-by-step explanation:
Total number of students = 10 students.
Given data, 1.1, 5.2, 3.6, 5.0, 4.8, 1.8, 2.2, 5.2, 1.5, 0.8
To find the mean, at first we have to take the sum of all given data and then divide with the number of students.
Let the data is X, = 1.1, + 5.2, + 3.6, + 5.0, + 4.8, + 1.8, + 2.2, + 5.2, + 1.5, + 0.8 = 31.2
Mean = 31.2 / 10 = 3.12
Answer:
Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms"
Also they can have one or more terms, but not an infinite number of terms.
These are polynomials:
3x
x − 2
−6y2 − ( 79)x
3xyz + 3xy2z − 0.1xz − 200y + 0.5
512v5 + 99w5
5
(Yes, "5" is a polynomial, one term is allowed, and it can be just a constant!)
These are not polynomials
3xy-2 is not, because the exponent is "-2" (exponents can only be 0,1,2,...)
2/(x+2) is not, because dividing by a variable is not allowed
1/x is not either
√x is not, because the exponent is "½" (see fractional exponents)
But these are allowed:
x/2 is allowed, because you can divide by a constant
also 3x/8 for the same reason
√2 is allowed, because it is a constant (= 1.4142...etc)
Monomial, Binomial, Trinomial
There are special names for polynomials with 1, 2 or 3 terms:
monomial, binomial, trinomial
Variables
Polynomials can have no variable at all
Example: 21 is a polynomial. It has just one term, which is a constant.
Or one variable
Example: x4 − 2x2 + x has three terms, but only one variable (x)
Or two or more variables
Example: xy4 − 5x2z has two terms, and three variables (x, y and z)
What is Special About Polynomials?
Because of the strict definition, polynomials are easy to work with.
For example we know that:
If you add polynomials you get a polynomial
If you multiply polynomials you get a polynomial
So you can do lots of additions and multiplications, and still have a polynomial as the result.
Also, polynomials of one variable are easy to graph, as they have smooth and continuous lines.
Example: x4−2x2+x
x^4-2x^2+x
See how nice and
smooth the curve is?
You can also divide polynomials (but the result may not be a polynomial).
Degree
The degree of a polynomial with only one variable is the largest exponent of that variable.
Example:
4x3-x-3 The Degree is 3 (the largest exponent of x)
For more complicated cases, read Degree (of an Expression).
Standard Form
The Standard Form for writing a polynomial is to put the terms with the highest degree first.
Example: Put this in Standard Form: 3x2 − 7 + 4x3 + x6
The highest degree is 6, so that goes first, then 3, 2 and then the constant last:
x6 + 4x3 + 3x2 − 7
You don't have to use Standard Form, but it helps.
