Question

If the mean of \[20,24,36,26,34\] and \[k\] is \[30\] then find \[k\].

Answer 1

Hint: We know that the mean is the sum of total terms divided by total number of terms.
At first, we will find the sum of the given terms.
Then we will divide the sum by the number of terms.
Hence, we can find the mean of the data.
Using the formula of mean we can find the value of \[k\].

Complete step-by-step solution:
The given data are: \[20,24,36,26,34\] and \[k\]
The mean of the given data is \[30\].
We have to find the value of \[k\].
We know that the mean is the sum of total terms \[ \div \] total number of terms.
Here, the sum of total terms \[ = 20 + 24 + 36 + 26 + 34 + k\]
Simplifying we get, the sum of total terms \[ = 140 + k\]
Total number of terms\[ = 6\]
The mean of the six terms is \[30\].
According to the problem,
\[\dfrac{{140 + k}}{6} = 30\]
Solving we get,
$\Rightarrow$\[140 + k = 30 \times 6\]
Simplifying we get,
$\Rightarrow$\[k = 180 - 140\]
Simplifying again we get,
$\Rightarrow$\[k = 40\]

Hence, the value of \[k\] is \[40\].

Note: The mean (or average) is the most popular and well-known measure of central tendency. It can be used with both discrete and continuous data, although its use is most often with continuous data.
The mean is equal to the sum of all the values in the data set divided by the number of values in the data set.
Let us consider, we have \[n\] values in a data set and they have values \[{x_1},{x_2},...,{x_n}\], the sample mean, usually denoted by \[\overline x \] (pronounced "\[x\] bar"), is:
\[\overline x = \dfrac{{{x_1} + {x_2} + ... + {x_n}}}{n}\]
This formula is usually written in a slightly different manner using the Greek capital letter, \[\sum \], pronounced "sigma", which means "sum of...":
\[\overline x = \dfrac{{\sum\limits_{i = 1}^n {{x_i}} }}{n}\]