Look at the picture
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Which of the following is the formula used to calculate the variance of a set of data
2 answers:
Answer:
(A) s^{2}=\frac{1}{n-1}\sum_{i}^{n}(x_{i}-\bar{x})^{2}
Step-by-step explanation:
Variance is the expectation of the squared deviation from the mean of x. Variance of the set of data can be discrete, continuous or mixed.
In order to calculate the variance of the set of the provided data, we need = Terms in set of data,
\bar{x}= Sample mean
∑= sum,
n= sample size.
The variance can be calculated as:
s^{2}=\frac{1}{n-1}\sum_{i}^{n}(x_{i}-\bar{x})^{2}
where is the variance and is always measured in squared units.
The correct formula is option (A),since it consists of summation of the square of the difference of the terms in the data and the mean, also variance is the measure of how far is each value in the given data from the mean, which is the correct formulation of the variance.
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Answer:
See the proof below.
Step-by-step explanation:
What we need to proof is this: "Assuming X a vector space over a scalar field C. Let X= {x1,x2,....,xn} a set of vectors in X, where . If the set X is linearly dependent if and only if at least one of the vectors in X can be written as a linear combination of the other vectors"
Proof
Since we have a if and only if w need to proof the statement on the two possible ways.
If X is linearly dependent, then a vector is a linear combination
We suppose the set is linearly dependent, so then by definition we have scalars
in C such that:
And not all the scalars are equal to 0.
Since at least one constant is non zero we can assume for example that , and we have this:
We can divide by c1 since we assume that and we have this:
And as we can see the vector can be written a a linear combination of the remaining vectors
. We select v1 but we can select any vector and we get the same result.
If a vector is a linear combination, then X is linearly dependent
We assume on this case that X is a linear combination of the remaining vectors, as on the last part we can assume that we select and we have this:
For scalars defined in C. So then we have this:
So then we can conclude that the set X is linearly dependent.
And that complet the proof for this case.
Answer:
40% students play the saxophone.
Step-by-step explanation:
Given:
Total Number of students who play woodwind instrument = 45
Number of students who play saxophone = 18
We need to find the percent of students who play saxophone.
Solution:
Now we can say that;
To find the percent of students who play saxophone we will divide Number of students who play saxophone by Total Number of students who play woodwind instrument and the multiply by 100.
framing in equation form we get;
percent of students who play saxophone =
Hence 40% students play the saxophone.