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Find the missing number in the data set given below with the MEAN provided

5, 8, , 12, 3

The MEAN is 7.8

Sagot :

VectorFundament120idn

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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Answer:

The missing value is 11.

Step-by-step explanation:

Given:

  • Given data set is 5,8,12,3.

To Find:

  • Mean of the given data set.

Formula used:

  • Mean = Sum of all data/Total no. of data

Let the missing value be x

Using the formula, we have

7.8 = (5+8+x+12+3)/5

7.8= (28+x)/5

39 = 28+x

x = 11

So, the missing value is 11.

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