The following observations have been arranged in ascending order. if the median of the data is 22, then find the value of the 6th observation.

12,14,16,18,x-1, x+3,30,32,35,41

  24

Step-by-step explanation:

The median is the middle number of the set.  If the set contains an even number of terms, then the median is the average of the two middle numbers.

{12, 14, 16, 18, x-1, x+3, 30, 32, 35, 41}

Cross out the end terms to find the median: {X, X, X, X, x-1, x+3, X, X, X, X}

The median is the average of the two middle numbers (x-1 and x+3).

The 6th term is x+3  ⇒  21 + 3   = 24

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

answer: 4  

the square root of 16 is 4. it is a very simple mathematic concept. a square root when a number multiplied by itself will result in a number. here, the number 16 comes when 4 is multiplied by 4. hence the square root of 16 is 4. you can always figure out a square root by the inverse operation of squaring.