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Find the average of \[80,90,100,110,120,130.\]
A. 100
B. 105
C. 110
D. 115

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Last updated date: 20th Jun 2024
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Answer
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Hint: Here we have to find the average of the given set of observations. Mean is a statistical value in statistics and probability theory. Mean is just the average of the given set of observations which is given by the ratio of the sum of all the observations to the total number of observations. Here given a set of observations which are numbers of sequences with a common difference.

Complete step-by-step solution:
Mean is the average of the given set of observations, which is mathematically expressed as:
$ \Rightarrow \overline x = \dfrac{{\sum\limits_i {{x_i}} }}{n}$
Where $\overline x $ is the mean of the data.
$\sum\limits_i {{x_i}} $= sum of the observations given in the set of data.
$n$= total no. of observations in the given set of data.
Here the given set of observations are:
\[ \Rightarrow 80,90,100,110,120,130.\]
The total number of the above set of observations are 6.
$\therefore n = 6$
$ \Rightarrow \sum\limits_i {{x_i}} = \sum\limits_{i = 1}^6 {{x_i}} $, as there are 6 observations in total.
Now calculating the average of the given set of observations, as given below:
$ \Rightarrow \overline x = \dfrac{{\sum\limits_{i = 1}^6 {{x_i}} }}{6}$
$ \Rightarrow \overline x = \dfrac{{80 + 90 + 100 + 110 + 120 + 130}}{6}$
$ \Rightarrow \overline x = \dfrac{{630}}{6}$
$ \Rightarrow \overline x = 105$
$\therefore \overline x = 105$

Hence the correct option is B.

Note: Here used the general arithmetic mean formula to find the value of the average of the given set of observations. Mean is the formal name of the average, it is also called as the arithmetic mean. It is always important to remember that to consider the correct number of total observations, as it plays a major role in finding the mean.