The mean and standard deviation of 63 children on an average test are respectively 27.6 and
7.1. To them are added a new group of 26 who have less training and whose mean is 19.2 and standard deviation is 6.2. How will the value of combined group differ from those of the original 63 children as to mean and standard deviation? 

Asked by deepanshi bansal | 5th Nov, 2014, 07:45: PM

Expert Answer:

S tan d a r d space D e v i a t i o n comma space S subscript 1 equals 27.6 cross times 63 S tan d a r d space D e v i a t i o n comma space S subscript 2 equals 19.2 cross times 26 m e a n space o f space t h e space c o m b i n e d space g r o u p equals fraction numerator 27.6 cross times 63 plus 19.2 cross times 26 over denominator 63 plus 26 end fraction equals fraction numerator 1738.8 plus 499.2 over denominator 8 9 end fraction equals 25.14 V a r i a n c e comma space V subscript 1 equals 7.1 squared equals 50.41 V a r i a n c e comma space V subscript 2 equals 6.2 squared equals 38.44 V a r i a n c e comma V subscript 1 equals 1 over 63 sum x subscript i squared minus left parenthesis m e a n right parenthesis squared rightwards double arrow 1 over 63 sum x subscript i squared equals 50.41 plus 27.6 squared rightwards double arrow sum x subscript i squared equals 812.17 cross times 63 equals 51166.71 V a r i a n c e comma V subscript 2 equals 1 over 26 sum x subscript i squared minus left parenthesis m e a n right parenthesis squared rightwards double arrow 1 over 26 sum x subscript i squared equals 38.44 plus 19.2 squared rightwards double arrow sum x subscript i squared equals 407.8 cross times 26 equals 10584.08 V a r i a n c e space o f space c o m b i n e d space g r o u p comma V a r i a n c e comma space V equals 1 over 89 sum left parenthesis x subscript 1 i end subscript squared plus x subscript 2 i end subscript squared right parenthesis minus left parenthesis m e a n right parenthesis squared equals 1 over 89 left parenthesis 51166.71 plus 10584.08 right parenthesis minus left parenthesis 25.14 right parenthesis squared space equals fraction numerator 61750.79 over denominator 89 end fraction minus 632.012 equals 693.83 minus 632.012 equals 61.82 S tan d a r d thin space D e v i a t i o n equals square root of 61.82 end root equals 7.86 M e a n space equals space 25.14
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Answered by Prasenjit Paul | 6th Nov, 2014, 02:26: PM