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Method
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Combined Sd Method:
- Find Combined mean `bar X_(12)`
- Find Combined Sd `(sigma_(12) = sqrt(( N_1 * (sigma_1^2 + d_1^2) + N_2 * (sigma_2^2 + d_2^2) )/( N_1 + N_2 )))`
- Find Combined Sd `(sigma_(12) = sqrt(((N_1 - 1) * sigma_1^2 + (N_2 - 1) * sigma_2^2 + (N_1 * N_2)/(N_1 + N_2) * (bar x_1^2 + bar x_2^2 - 2 bar x_1 bar x_2))/(N_1 + N_2 - 1)))`
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- Find Combined Mean and Standard deviation`N_1=40,sum X_1=10,V_1=1`
`N_2=60,sum X_2=15,V_2=2`
- Find Combined Mean `N_1=80,sum X_1=520`
`N_2=20,sum X_2=420`
- Find Combined Mean `N_1=20,sum X_1=50`
`N_2=50,sum X_2=12`
- Find Combined Mean and Standard deviation`N_1=40,sum X_1=400,V_1=1`
`N_2=60,sum X_2=900,V_2=4`
- Find Combined Mean `N_1=80,sum X_1=41600`
`N_2=20,sum X_2=8400`
- Find Combined Mean `N_1=20,sum X_1=1000`
`N_2=50,sum X_2=600`
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2. Find X2 from Combined Mean X12 and X1
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- Combined Mean `bar X_(12) = 40, bar X_1 = 10 , N_1 = 1, N_2 = 60`, find `bar X_2`
- Combined Mean `bar X_(12) = 80, bar X_1 = 520 , N_1 = 20, N_2 = 420`, find `bar X_2`
- Combined Mean `bar X_(12) = 20, bar X_1 = 50 , N_1 = 50, N_2 = 12`, find `bar X_2`
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Solution
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Solution provided by AtoZmath.com
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Find Combined Mean and Standard deviation
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1. Find the combined Standard Deviation from the following data.
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B |
| number of Observations |
40 |
60 |
| Average |
10 |
15 |
| S.D. |
1 |
2 |
2. Find the combined Standard Deviation from the following data.
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A |
B |
| number of Observations |
100 |
150 |
| S X |
25000 |
42000 |
| Variance |
100 |
40.96 |
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