The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is:
Solutions · 1
Official solution
Initially we have 16 observations and among them one is 16.
So, we have 15 unknowns. Let those are a1,a2,a3.....a15
\[\therefore\,\,\,\] Mean of 16 datal set
\[ = {{{a_1} + {a_2} + .....{a_{15}} + 16} \over {16}}\]
According to the question,
\[{{{a_1} + {a_2} + .....{a_{15}} + 16} \over {16}} = 16\]
\[ \Rightarrow {a_1} + {a_2} + ...... + {a_{15}} = 256 - 16 = 240\]
Now we deleted 16 and replaced by there new numbers 3,4, and 5.
So, new mean
\[ = {{{a_1} + {a_2} + .......{a_{15}} + \left( {3 + 4 + 5} \right)} \over {18}}\]
\[ = {{240 + \left( {3 + 4 + 5} \right)} \over {18}}\]
\[ = {{240 + 12} \over {18}}\]
=14