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Descriptive Statisticsmedium
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A researcher surveys two schools:

  • School A: nA=100n_A = 100nA​=100 students, variance = sA2=25s_A^2 = 25sA2​=25 cm²
  • School B: nB=200n_B = 200nB​=200 students, variance = sB2=36s_B^2 = 36sB2​=36 cm²

The pooled variance formula is: sp2=(nA−1)sA2+(nB−1)sB2nA+nB−2s_p^2 = \frac{(n_A - 1)s_A^2 + (n_B - 1)s_B^2}{n_A + n_B - 2}sp2​=nA​+nB​−2(nA​−1)sA2​+(nB​−1)sB2​​

What is the combined variance?