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To find the unknown value 'x' in the series 3.8, 4.2, 5.3, x, we'll use the formula for the mean of a set of numbers. The formula for the mean (average) of a set of numbers is the sum of the numbers divided by the quantity of the numbers.
We are given that the mean of the four numbers is 4.8, so the sum of all four numbers is 4.8 multiplied by 4, since there are four numbers in our series. Here's how we calculate it:
Count of numbers = 4 Mean (average) = 4.8
Sum of all numbers = Mean × Count of numbers Sum of all numbers = 4.8 × 4 Sum of all numbers = 19.2
Now we know the sum of all the numbers is 19.2. To find the missing number x, we subtract the known numbers from the sum:
Sum of known numbers = 3.8 + 4.2 + 5.3 Sum of known numbers = 13.3
Subtract the sum of known numbers from the total sum to find x:
x = Sum of all numbers - Sum of known numbers x = 19.2 - 13.3 x = 5.9
So, the missing number x is 5.9.