Which pair of numbers , if included in the data set below , would change the mean of the data (20,21,22,25,27) options (23,23) (22,24) (19,39) (15,31)

Question

Which pair of numbers , if included in the data set below , would change the mean of the data (20,21,22,25,27) options (23,23) (22,24) (19,39) (15,31)

Answer 1

The mean of (20, 21, 22, 25, 27) is 23.  This is (20+21+22+25+27)/5

 

The mean of (20, 21, 22, 25, 27, 23, 23) is 23.  This is (20+21+22+25+27+23+23)/7

       Note:  deliberately not sorted

 

The mean of (20, 21, 22, 25, 27, 22, 24) is 23.  This is (20+21+25+27+22+24)/7

 

The mean of (20, 21, 22, 25, 27, 19, 39) is 24.7.  This is (20+21+22+25+27+19+39)/7

     Note that 19+39 = 58 and 2*23=46, so the mean goes up.

 

The mean of (20, 21, 22, 25, 27, 15, 31) is 23.  This is (20+21+22+25+15+31)/7

     Note that 15+31 = 46 and 2*23=46, so the mean stays the same.