Question

The mean of 18, 28, x, 32, 14 and 36 is 23. Find the value of x and Sum of data.

Answer 1

Hint: We need to solve this question by using the concept of mean in statistics. Mean for a set of numbers is nothing but the average for the given set of data which can be calculated by adding all the terms in the set of data and dividing it by the total number of terms in the data set. Using this concept, we calculate the value of x by using this mean formula.

Complete step by step answer:
In order to solve this question, let us first give the formula to calculate the average of a set of numbers. Average or mean is nothing but the sum of the numbers divided by the total number of terms in the data set.
The formula for mean is given as,
\[\Rightarrow \text{Mean=}\dfrac{{{x}_{1}}+{{x}_{2}}+........{{x}_{n}}}{n}\]
Given data is 18, 28, x, 32, 14 and 36, we know the number of terms id 6. We calculate the mean by substituting in the above formula.
\[\Rightarrow \text{Mean=}\dfrac{18+28+x+32+14+36}{6}\]
We also know the mean for the given data is already calculated as 23.
Substituting this in the above equation too,
\[\Rightarrow 23\text{=}\dfrac{18+28+x+32+14+36}{6}\]
Multiplying both sides by 6 and adding all the terms in the numerator on the right-hand side,
\[\Rightarrow 23\times 6=x+128\]
On further calculation,
\[\Rightarrow 138=x+128\]
Taking 128 on left-hand side, then we get
\[\Rightarrow x=138-128\]
Subtracting the terms on the right-hand side, we get the value of x as,
\[\Rightarrow x=10\].
Hence, the value of x if 18, 28, x, 32, 14 and 36 have a mean of 23 is 10.
\[Sum\text{ }of\text{ }data=~18+28+x+32+14+36\]
Substituting the value of x and adding all the values in sum of data, then we get
\[Sum\text{ }of\text{ }data=~138\].

Note: We need to note that the average of a set of numbers is the same as mean. It is a very basic statistical concept in mathematics. We need to take care while considering the mean for negative numbers. Remembering the concept and formulas are important in this topic.