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3 years ago

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Which better describes the data set, the mean or the median?

2 answers:

Xelga [282]3 years ago

8 0

The median...(hope it helps)

Serga [27]3 years ago

3 0

You would need to give us the data set to answer this question. I'm assuming this is a stats question which means I'd need to see what set of data you are working with to determine if the mean or median is best to describe the center. The meadian is resistant to outlying values while the mean is not. Therefore the meadian is a better describer for skewed distributions. Whenever you have outliers the dataset is skewed. Take a look at the shape of the data. Does it look skewed? You can make a simple graph with the data points to determine if there are outliars if you aren't able to tell just from looking at the data. (Again I don't know what data you are working with, but I hope this helped)

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Trig proofs with Pythagorean Identities.

lorasvet [3.4K]

To prove:

$$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1$

Solution:

$$LHS = \frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}$

Multiply first term by $\frac{1+cos x}{1+cos x}$ and second term by $\frac{1-cos x}{1-cos x}$ .

$$= \frac{1(1+\cos x)}{(1-\cos x)(1+\cos x)}-\frac{\cos x(1-\cos x)}{(1+\cos x)(1-\cos x)}$

Using the identity: $(a-b)(a+b)=(a^2-b^2)$

$$= \frac{1+\cos x}{(1^2-\cos^2 x)}-\frac{\cos x-\cos^2 x}{(1^2-\cos^2 x)}$

Denominators are same, you can subtract the fractions.

$$= \frac{1+\cos x-\cos x+\cos^2 x}{(1^2-\cos^2 x)}$

Using the identity: $1-\cos ^{2}(x)=\sin ^{2}(x)$

$$= \frac{1+\cos^2 x}{\sin^2x}$

Using the identity: $1=\cos ^{2}(x)+\sin ^{2}(x)$

$$=\frac{\cos ^{2}x+\cos ^{2}x+\sin ^{2}x}{\sin ^{2}x}$

$$=\frac{\sin ^{2}x+2 \cos ^{2}x}{\sin ^{2}x}$ ------------ (1)

$RHS=2 \cot ^{2} x+1$

Using the identity: $\cot (x)=\frac{\cos (x)}{\sin (x)}$

$$=1+2\left(\frac{\cos x}{\sin x}\right)^{2}$

$$=1+2\frac{\cos^{2} x}{\sin^{2} x}$

$$=\frac{\sin^2 x + 2\cos^{2} x}{\sin^2 x}$ ------------ (2)

Equation (1) = Equation (2)

LHS = RHS

$$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1$

Hence proved.

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4 years ago

Jack draw an angle that is 27 out of 36 of a circle.What is the measure of the angle in degrees

34kurt

let's recall that a circle has a total of 360°.

now, Jack drew "27 out of 36", namely 27/36.

what's 27/36 of 360°? well, is simply their product.

$\bf \cfrac{27}{36}\cdot 360\implies 27\cdot \cfrac{360}{36}\implies 27\cdot 10\implies 270$

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