The following data give the prices of seven textbooks randomly selected from a university bookstore. $93 $173 $107 $125 $56 $163 $144 a. Find the mean for these data. Calculate the deviations of the data values from the mean. Is the sum of these deviations zero? Mean = $ 123 Deviation from the mean for $173 = $ 0 Sum of these deviations = $ -433 b. Calculate the range, variance, and standard deviation. [Round your answers to 2 decimal places.] Range = $ Variance = Standard deviation = $ Click if you would like to Show Work for this question: Open Show Work LINK TO TEXT

Mean = $123

Standard deviation = 10190

Variance = 1698

Step-by-step explanation:

Mean=?

      = sum of all numbers/ Total numbers

    a  =  93+173+107+125+56+163+144 / 7  = 861/7 = $123

Standard deviation=?

we know that = Sqareroot [ Sum (y)²] / N

we need deviation:

=    x-a         =  y   ;    y²                

  = 93-123 = -30  ;   900

   =173-123 = 50  ;    2500

  =107-123  =  -16 ;   256

   =125-123  = 2   ;    4

   =56-123   =  -67 ;   4489

   =163-123  =  40  ;   1600

   =144-123   =  21   ;   441

Sum of y²            =   10190.

  = Square root [  10190 / 7 ]

  =  38.1

Variance = ?

        = Sum ( y)² / N-1

        =  10190 / ( 7-1)

       = 10190 /6

     = 1698

Given :

The diagonals of rhombus ABCD intersect at E.

∠CAD = 20°.

To Find :

The angle ∠CDA.

Solution :

We know, diagonals of a rhombus bisects each other perpendicularly.

So, ∠DEA = 90°.

In triangle ΔEAD :

∠EAD + ∠AED + ∠EDA = 180°

20° + 90° + ∠EDA = 180°

∠EDA = 70°

Now, we know diagonal of rhombus also bisect the angle between two sides .

So, ∠CDA = 2∠EDA

∠CDA = 2×70°

∠CDA =140°

Therefore, ∠CDA is 140°.