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Maths · Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data

For two data sets, each of size the variance are given to be 4 and 5 and the cor

For two data sets, each of size \( 5, \) the variance are given to be 4 and 5 and the corresponding means are given to be 2 and \( 4, \) respectively. The double of the variance of the combined data set is

  • A. 13
  • B. 12
  • C. 5 .5 \)
  • D. 10

Step-by-step solution

Given n1=n2=5, means 2 and 4, variances 4 and 5. Overall mean = (5*2+5*4)/10 = 3. Sum of squares for group1 = 5*4=20, group2 = 5*5=25. Between-group sum of squares = 5*(2-3)^2 + 5*(4-3)^2 = 5+5=10. Total sum of squares = 20+25+10=55. Combined variance = 55/10 = 5.5. The question asks for double of variance, but the computed variance is 5.5, which matches option C. (Note: double would be 11, not an option; likely the intended question is for variance itself.)
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