Question

Find the arithmetic mean of the progression \[2,4,6,8,10\]
A) \[10\]
B) \[20\]
C) \[30\]
D) \[6\]

Answer 1

Hint: In this question we have to use the formula of arithmetic mean. Arithmetic mean is also known as arithmetic average. To calculate the value of arithmetic mean, we add up all the numbers. Then addition is divided by how many numbers there are. We can say that it is the sum divided by the count. We can find the value of arithmetic mean, or average, by adding up the scores and dividing the total by the number of counts.

Formula used: To calculate arithmetic mean, we have to take addition of all digits. After addition, the summation is divided by total number of terms. After that we will get the arithmetic mean of given terms. The formula to calculate arithmetic mean is
\[Arithmetic{\text{ }}mean = \dfrac{{sum{\text{ }}of{\text{ }}all{\text{ }}terms}}{{number{\text{ }}of{\text{ }}terms}} \\
   
 \]

Complete step-by-step answer:
Given: terms=\[2,4,6,8,10\], number of terms, \[n = 5\]
Therefore, \[
  Arithmetic{\text{ }}mean = \dfrac{{sum{\text{ }}of{\text{ }}all{\text{ }}terms}}{{number{\text{ }}of{\text{ }}terms}} \\
    \\
 \]
\[\overline X = \dfrac{{2 + 4 + 6 + 8 + 10}}{5}\]
\[ \Rightarrow \overline X = \dfrac{{30}}{5}\]
\[\therefore \overline X = 6\]

Hence, the average mean of \[2,4,6,8,10\] is \[6\]

Additional information: In given data, the sum of all of the numbers of a group, when divided by the number of items in given data is known as the Arithmetic Mean or Mean of the data.
Let \[{x_1},{x_2},{x_3},..........,{x_n}\]are n terms. Then arithmetic mean or arithmetic average is given by
\[ = \dfrac{{{x_1} + {x_2} + {x_3},.......... + {x_n}}}{n}\]
\[ = \dfrac{{\sum\limits_{i = 1}^n {{x_i}} }}{n}\]
Where, \[\sum\limits_{i = 1}^n {{x_i}} \]= sum of all terms
The arithmetic mean is denoted by \[\overline X \]. Hence, we can say that \[\overline X = \dfrac{{{x_1} + {x_2} + {x_3},.......... + {x_n}}}{n}\]
Please note that average is different from an Arithmetic Mean. An Arithmetic mean is totally different from a median. In statistics, mean is defined by the average of a set of data whereas the median is given by the middle value of the arranged set (ascending or descending)of data. Both mean and median values play an important role in data collection and organization.

Note: For arithmetic arranging data in ascending and descending order is not required. Ascending or descending order is only required in the median. Students make clear about mean and median.