Question

For certain data, the following information is available. Obtain the combined standard deviation.

	X	Y
Mean	13	17
S.D.	3	2
Size	20	30

Options

• 9.84

• 1.54

• 3.14

• 15.4

Answer 1

3.14

Explanation:

Here, `overlinex = 13, overliney = 17, sigma_x = 3, sigma_y = 2, n_x = 20, n_y = 30`

Combined mean `(overlinex_c) = (n_x overlinex + n_y overliney)/(n_x + n_y)`

= `(20(13) + 30(17))/(20 + 30)`

= `(260 + 510)/50 = 770/50`

= 15.4

Now, `d_x = overlinex - overlinex_c = 13 - 15.4 = -2.4`

`d_y = overliney - overlinex_c = 17 - 15.4 = 1.6`

∴ Combined standard deviation `(sigma_c)`

= `sqrt((n_x(sigma_x^2 + d_x^2) + n_y(sigma_y^2 + d_y^2))/(n_x + n_y))`

= `sqrt((20[3^2 + (-2.4)^2] + 30(2^2 + 1.6^2))/(20 + 30)) = 3.14`