which of the following choices is the standard deviation of the sample shown below here 17,18,19,20,21

1 answer:

4 0

Where are "the following choices?" Please don't overlook sharing this info with possible helpers. Thank you.

This kind of assignment can be one on a calculator; I typed in stdDev(17,18,19,20,21) an got std dev= 1.58.

working backward, the variance is the square of that: 2.5.

To find the variance: Find the mean of the given set of numbers. It is

17+18+19+20+21 95
------------------------- = ----- = 19
5 5

and then calculate the deviations of all 5 numbers from the mean:

17-19=-2
18-19= -1
19-19=0
20-19 = 1
21-19=2

Then sum up the squares of these: 4+1+0+1+4 = 10
Finally, divide this result by 5-1 (one less than the # of data points):

10
------- = 2.50 (variance)
(5-1)

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Can someone please explain to me how to get this answer?

SIZIF [17.4K]

Answers:
A = 120
b = 45.0
c = 33.2

Side Note: only one triangle is possible
See attached for a visual. I used GeoGebra to draw the triangle.

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Explanation:

We are given the following information
B = 35
C = 25
a = 68

We need to find the following
A, b, c

where the lower case letters represent the side lengths; the upper case letters are the angles. The angles are opposite their corresponding sides. For instance, side lowercase b is opposite angle uppercase B. The other letters are positioned the same way.

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First use the idea that for any triangle, the three angles (A,B,C) must add to 180 degrees
A+B+C = 180
Replace B and C with 35 and 25. Solve for angle A
A+35+25 = 180
A+60 = 180
A+60-60 = 180-60
A = 120

Now that we know the three angles A = 120, B = 35, C = 25, we can find the missing sides 'b' and 'c'

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We will use the law of sines to find side b
sin(A)/a = sin(B)/b
sin(120)/68 = sin(35)/b
b*sin(120) = 68*sin(35) <<--- cross multiply
b = 68*sin(35)/sin(120)
b = 45.037013350222 <<--- use a calculator; this value is approximate
b = 45.0 <<--- round to the nearest tenth

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Do the same for side c
sin(A)/a = sin(C)/c
sin(120)/68 = sin(25)/c
c*sin(120) = 68*sin(25) <<--- cross multiply
c = 68*sin(25)/sin(120)
c = 33.1838323365404 <<--- use a calculator; this value is approximate
c = 33.2 <<--- round to the nearest tenth