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I hope Rom will give you a detailed answer, but there are 10 possible choices out of 90 values, so 10/90=1/9. 

First one.....add the data values

Each sector of the circle will occupy this many degrees  =   

Single Data Value /  Sum of Data Values  x 360

So...for example....the Magpie would occupy  15 /72 x 360  =  5 / 24 x 360  = 75°

It should look like this  when you finish:

Cool.....got it....thanx !  ~EP

Thanks Ginger  

OK, ant  !!!!

THX, ant  !!!!

We can first find the mean, which is 80/10=8.

Now, for each number: subtract the Mean and square the result!

So, (15-8)^2, (8-8)^2, (14-8)^2, (7-8)^2, (6-8)^2, (8-8)^2, (2-8)^2, (8-8)^2, (9-8)^2, (3-8)^2

Which is, 49, 0, 36, 1, 4, 0, 36, 0, 1, 25

Now, find the mean, which is 49+0+36+1+4+0+36+0+1+25/10=15.2!

15  8   14    7   6    8    2   8   9    3

The mean is 8

To find the variance...take the average of the squared differences from the mean

So.......we would have

(15 - 8)^2  +  (8 - 8)^2 + ( 7 - 8)^2 + .......+ (3 - 8)^2

___________________________________________

                              10

This ends up being    15. 2   =    [ population variance ]

First, create six spots for your number and label them 100000x, 10000y, 1000z, 100x, 10y, z. Add everything up, and see what you can do from there! 

Thank you so much, CPhill!

The computer finds it by using Newton-Raphson iteration and interpolation method. Use this online calculator to find b for you:  https://www.johndcook.com/interpolator.html

Notice, EP, that all rotations of any arrangement are the same.....so.....a Repub assigned to any one seat can be in this same seat no matter the rotation....the only difference in the arrangements  are the number of ways that the other people can be seated around him  [ keeping in mind that we must have alternating seating patterns of R - D - R - D, etc ]

To see this more easily....in a simplified example....suppose that we have 4  people seated at a table

One arrangement is  

                                         1

                                 4            2

                                       3

This is the same arrangement [ with respect to rotations ] as 

                                          4

                                 3             1

                                        2    

So.....if we anchor  the first person at the " top "...the only difference in arrangements [ with respect to rotations ] are the ways the other three people are  seated around him.....note that another possible arrangement is

                                            1

                                    3             4

                                           2

In right triangle ABC, AB=9, BC=13 ......

Yep, 2.5 is right.

Can you send me the way?

b=1 / 5.56962077581

Hmm, 

I'm not sure.

Slight correction     2.5     not 2/5 as cphil found  (or maybe he meant  5/2 instead of 2/5)

Hmmmm.....isn't it 5! x 5!  

5 choices for first seat   5 choices second seat   4 choices third seat   etc etc

5! x 5!

I always seem to get these quite wrong!     ~EP

If each member sits next to two members of the other party, they must just alternate D - R - D - R, etc

So...."anchor" one member, say, a Republican,  in any position

Going counter-clockwise  [ we could also go in the other direction ], we have

5 choices for the next seat [ one of 5 Dems ], 4 for the next [ one of 4 remaining Repubs ], 4 for the next [ one of the 4 remaining Dems, 3 for the next [ one of the 3 remaining Repubs ]....etc.

So...the number of possible arrangements  = 5! * 4!  =  120 *24  =  2880

 [ OAB]  =  30

And since AB = 10....then the altitude  of triangle  OAB  is

30  = (1/2) AB * altitude

60 = 10 * altitude

6 = altitude

And AB is a chord of the circumcircle.....and the altitude of OAB meets chord AB at right angles, so it bisects AB  ....so 1/2AB  = 5

And this altitude and 1/2 AB = 5   will form the legs of a right triangle with the circumradius as the hypotenuse

So

circumradius  =   sqrt  [ 6^2 + 5^2 ]   =  sqrt [ 36 + 25 ]  =  sqrt (61)

Thank you, CPhill! I understand it better, now!

The median  of a right triangle drawn to the hypotenuse from the right angle has the same measure as 1/2 of the hypotenuse

We have a 3 - 4 - 5 right triangle wth BC  as the hypotenuse = 5

So   MB  = AM  =  (1/2) * 5   =   2.5

The diagonals of a rectangle are congruent and  bisect each other....