From the combined standard deviation, with the mean, and standard
deviation of the data sets, the required variance can be found.
Reasons:
The given data information are;
Mean of the first set of observation, = 9.0
Standard deviation of the the first set, σ₁ = 4.0
Sample size of second observation, n₂ = 20
Mean of second sample, = 10
Standard deviation of the combined set, σ₁₂ = 3.0
Sample size of combined set of observation, n₂ = 35
Solution:
The number of elements in the second sample, n₁ = 35 - 20 = 15
The standard deviation of the combined set is given by the formula;
Where;
Therefore;
d₁ = -
d₂ = -
Therefore;
Solving gives;
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