The missing number in the data set is 11.
What is mean value?
Mean value or Average value is a total data divided by the number of data (how many elements are there). In mathematics, it can be expressed as the equation of:
[tex]\displaystyle{\bar x = \dfrac{x_1+x_2+x_3+\dots + x_n}{N}}[/tex]
We define [tex]\displaystyle \bar x[/tex] (x bar) as mean value, N as number of data and the sum is summation of numerical data.
Solution
First, we know that there are 5 numerical data in the data set given ; therefore, N = 5. The question also gives that the mean value is 7.8 and therefore [tex]\displaystyle \bar x[/tex] = 7.8
Substitute the known information in the formula:
[tex]\displaystyle{7.8 = \dfrac{5+8+x+12+3}{5}}[/tex]
Since we are finding the missing data, solve for x:
[tex]\displaystyle{7.8 \cdot 5 = 28+x}\\\\\displaystyle{39=28+x}\\\\\displaystyle{39-28=x}\\\\\displaystyle{11=x}[/tex]
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