Answer:
The missing number on the given data set is 12.
Step-by-step explanation:
Here, the set of data = 18,16_,9,12,23
Let us assume the missing number in the data = m
The mean of the data = 15
Total number of observations = 6
Now, Sum of the data = 18 + 16 + m + 9+ 12+ 23 = 78 + m
Also, ![\textrm{ Mean of the given Data} = \frac{\textrm{Sum of all observation in the data}}{\textrm{Total number of observations}}](https://tex.z-dn.net/?f=%5Ctextrm%7B%20Mean%20of%20the%20given%20Data%7D%20%20%3D%20%5Cfrac%7B%5Ctextrm%7BSum%20of%20all%20observation%20in%20the%20data%7D%7D%7B%5Ctextrm%7BTotal%20number%20of%20observations%7D%7D)
![\implies 15 = \frac{78+ m}{6} \\or, 15(6) = 78 + m\\\implies m = 90 -78 = 12](https://tex.z-dn.net/?f=%5Cimplies%2015%20%3D%20%5Cfrac%7B78%2B%20m%7D%7B6%7D%20%5C%5Cor%2C%2015%286%29%20%3D%2078%20%2B%20m%5C%5C%5Cimplies%20m%20%3D%2090%20-78%20%3D%2012)
or, m = 12
Hence, the missing number on the given data set is 12.