Let `x_1, x_2, ,x_n` be `x_n` observations. Let `y_i=a x_i+b` for i=1,2,...,n where a and b are constants. If the mean of `x_i's` is 48 and their standard deviation is 12, the mean of `y_i 's` is 55 and standard deviation of `y_i's` is 15, the values of a and b are

Explanation

It is given that ,

`y_i = ax_i+b`

`barX = 48, sigma_x = 12`

`barY = 55 and sigma_y = 15`

Now, as , ` y_i = ax_i+b`

`:. barY = abarX + b`

`=>55 = 48a+b ->(1)`

Now, their variances will also be equal.

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