1. Combined Mean `bar X_(12) = 40, bar X_1 = 10 , N_1 = 1, N_2 = 60`, find `bar X_2`
Solution:
Combined Mean :
`bar x_(12) = ( N_1 * bar x_1 + N_2 * bar x_2 )/( N_1 + N_2)`
`40 = ( 1 * 10 + 60 * bar x_2)/( 1 + 60)`
`40 = ( 10 + 60 * bar x_2)/( 61)`
`40 * 61= 10 + 60 * bar x_2`
`2440= 10 + 60 * bar x_2`
` 60 * bar x_2=2440 - 10`
` 60 * bar x_2=2430`
` bar x_2=2430/60`
` bar x_2=40.5`
2. Combined Mean `bar X_(12) = 80, bar X_1 = 520 , N_1 = 20, N_2 = 420`, find `bar X_2`
Solution:
Combined Mean :
`bar x_(12) = ( N_1 * bar x_1 + N_2 * bar x_2 )/( N_1 + N_2)`
`80 = ( 20 * 520 + 420 * bar x_2)/( 20 + 420)`
`80 = ( 10400 + 420 * bar x_2)/( 440)`
`80 * 440= 10400 + 420 * bar x_2`
`35200= 10400 + 420 * bar x_2`
` 420 * bar x_2=35200 - 10400`
` 420 * bar x_2=24800`
` bar x_2=24800/420`
` bar x_2=59.0476`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
