Here, Calculation of median

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Here,  Arranging the given data in ascending order, 5, 10, 15, 20, 25, 30, 35. Let assumed a = 20 Calculation of standard deviation:  

Here, Let assumed a = 15.    Calculation of standard deviation and its coefficient:  

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Here, Calculation of mean deviation its coefficient:

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Here,  Calculation of standard deviation,  Let the assumed mean be 50.   

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Here, Let ,assumed mean ,A = 30.                 Calculation of standard deviation:

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Here, Calculation of mean deviation:

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Here, Calculation of MD and its coefficient:

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Here, Calculation of mean deviation from median:

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Calculation of standard deviation:  

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Here, Calculation of mean deviation from median

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Here, Calculation of mean deviation

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Here, Let assumed mean (A) be 30. Calculation of standard deviation and its coefficient,  

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Calculation of mean deviation from median:

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Here, Calculation of mean deviation:

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Here,    Calculation of standard deviation

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Here,   Calculation of standard deviation:  

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Here,   Let assumed mean (a) = 25.               Calculation of standard deviation and its coefficient,

Here, Calculation of mean deviation from median:

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Here, Calculation of standard deviation:  

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Here,  P(-2, 0), Q(-5, 1), R(-4, 4) and S(-1, 3) So, the object in the matrix form = -2-5-4-10143. P'(-2, -2), Q'(-3, -7), R'(4, -12) and S'(5, -7)  So, the image in matrix form = -2-345-2-7-12-7. Let   M .....

Here, co- ordinates of ∆ABC are: A(3, 6), B(5, -3) and C(-4, 2) So, object in matrix form =  35-46-32    . Co-ordinates of image are, A(-3, -6), B'(-5, 3), C'(4, -2) Image in matrix form = -3-54-63-2      .....

Here,  A(2, 0), B(5, 1), C(4, 4) and D(1, 3)  The object in matrix form = 25410143. Image: A'(2, 2), B'(7, 3), C'(12, -4), D'(7, -5) Image in matrix form = 2712723-4-5. Let M = abcd be required transeormation .....

Here, given vertices ∆PQR; P'(-3, -4), Q'(-4, -6) and R(-1, -8). Object in matrix form = 468341. Image in the matrix form = -3-4-1-4-6-8. Let  M = abcd be 2 × 2 transformation matrix then,       Image .....

Here, Object in matrix form = ab Image in matrix form = a+2b-3 Let xy be the 2 × 1 transformation matrix.  Then,      Object + M = Image  or, ab + xy= a+2b-3 or, a+xb+y = a+2b-3 Here, M = xy = 2-3 Again, Image = M + .....

Here, Object is matrix form = ab Image in matrix form = a+4b-5 Let xy be 2 × 1 matrix then,         M + object = Image  or, xy  + ab = a+4b-5 ∴ x+ay+b = a+4b-5 ∴   x = 4 and y = -5 .....

Here,  Object = 02320351    Image =  03510232 Let, M = abcd be 2 × 2 transformation matrix.  We know that,       Image =  M × Object or, 03510232 = abcd .....

Here, Let,M =   abcd is require 2 × 2 matrix and 01100011 is a unit square matrix.     Now, according to question,        M ⨉ O = I      abcd  01100011  = 04620132   .....

Here, given transformation matrix = 1001 and point (2, 4) object in matrix from = 24 We know that, Image = TM × Object                  = 100124        .....

Here,  W(0, 3), X(1, 1), Y(3, 2) and Z(2, 4). The object in matrix form = 01323124. Transformation matrix (TM) =   0-1-1   0. We know that,     Image = TM × object              .....

Here, Object in matrix form = ab Image in matrix form = -10-8 and M = 0-2-20 We know that,       Image = M × object  or, -10-8 = 0-2-20 × ab or,  -10-8 = 0-2b2a+0 ∴ -10-8 = -2b-2a Equating the .....

Let, A(x, y) be a point and A1(-x, y) be image after reflection on the line y-axis.  So,        (x, y)  →(-x, y)  i.e. –x = (-1)x + 0 ×  y and        y = 0 × x .....