CPhill

1    

92    97   53  90   95    98

Mean = Sum of the Values  / Number of Values  = 

[ 92 + 97 + 53 + 90 + 95    + 98  ]  /   6    =   87. 5

Variance  =  

(92 - 87. 5)   =  4.5    ⇒ 4.5^2  ⇒  20.25

(97 - 87.5)  =  9.5 ⇒ 9.5^2  =  90.25

(53 - 87.5)  = -34.5  ⇒ (-34.5)^2   = 1190.25

(90 - 87. 5) = 2.5 ⇒ 2.5^2  = 6.25 

(95 - 87.5) = 7.5 ⇒ 7.5^2 ⇒ 56.25

(98 - 87.5) = 10.5 ⇒ 10.5^2 ⇒ 110.25

Add the values in the last column  =  1473.5

Take this value and divide it by the number of data values  = 6

1473.5 / 6   =   245.58

The standard deviation is the square root of this  = 15.7

Second answer 

We have  a weighted average here :

[ Number of vehicles  ]  / [ Number of households  ]  =

[ 3*0   +  9*1 + 10*2  + 2*3  + 1*4  ]  / [ 3 + 9 + 10 + 2 + 1  ]  =

[ 0 + 9 + 20 + 6 + 4  ]  / [ 25 ]   =

[ 39 ] /  [ 25 ]   =

1.56   =  1.6  venicles per household

Look at the diagram, ACG

The area between chord BC  and the edge of the top circle can be found as

Area of sector ABC  - area of triangle ABC =

(1/4)pi (4)^2  - (1/2)(4^2)sin (90°)  =

[ 4pi  - 8 ] units^2

And due to symmetry.....we would have 8 of these areas....so....the total area of the shaded regions is

8 ( 4pi  - 8  )   =

[ 32 pi  - 64]  units ^2

The first fold results  in  the side of 11  being divided in half....so....we have the the dimensions

8.5  x  5.5

The second fold results in the side of 8.5 being divided in half...so...we have the dimensions

4.25 x  5.5

So....the longest side is   5.5 in

See my corrected answer, CHB....

Let the radius of the small circle  be r

Let the radius of the larger circle be R

45°  = pi/4  in rads          36°  =  pi/5   in rads

And the arc length, S, of the smalller circle can be expressed as

S  = r(pi/4)

But this is equal to the arc length of the larger circle that can be expressed as

S  = R(pi/5)

So....this implies that

r(pi/4)   = R(pi/5

r/4  = R/5                solve for R

R = (5/4)r  

So....the area of the smaller circle is   

pi * r^2        (1)

And the area of the larger circle is

pi * R^2  =  pi * [ (5/4)r ]^2   = pi (25/16)r^2    (2)

So....the ratio of the area of the smaller circle to the larger circle is just   (1)  / (2)  =

[ pi* r^2 ]  / [pi * (25/16) r^2 ] =

16  / 25

5.  This is pretty easy, NSS........

18  9   7   5   11   7  17  20  19   2   17   12   5   1   13   12    11   15   16   20

Order data from low-to-high...there are 20 values

1  2   5  5  7   7   9    11  11   12  12   13  15   16   17    17    18    19     20   20

To find the 30th percentile....multiply  .30 * 20    =  6    (this is the index)

The 6th number in the data set  is   7

Similary...to find the 90th percentile......multiply  .90 * 20   =  18    (this is the index )

The 18th number in the data set is 19

So.....the first answer is correct     

(BTW....there may be several  other acceptable  ways to do this )

2. The outlier is  38

Look at the graph here, Creeperhissboom :

Apparently..from the graph..the  range is   ([ 0, .2, .4, .6, .8,  1 )

CORRECTED ANSWER

15  13    9   9   7    1  11    10   13    1    13

Order the data

1   1    7     9    9    10    11     13    13     13     15

Mean  =  Sum of the Values  / Number of Values  =  102 / 11  =  9.27  = 9.3  

Median  =   Value in the middle =  10

Mode =  The value that appears the most often  =  13

The third answer is correct