Question

Arithmetic Mean is _____ affected by extreme values.
(a) Not
(b) Highly
(c) Less
(d) None of these

Answer 1

Hint: To solve this question, we will first define the Arithmetic Mean. Then we will consider a sample data set to express its average and see how the Arithmetic Mean is affected by the extreme values.

Complete step-by-step answer:
Suppose a data set, x, y and z are three values in a data set. Then the arithmetic mean of this data set will be $ \dfrac{x+y+z}{3} $ . We divide the sum by 3 because there are 3 elements in the data set.
Let us consider an example to understand the Arithmetic Mean better.
Suppose we have data set X, where X = {2, 8, 7, 4, 11, 9, 2, 5, 3}.
As we can see, the data set X has 9 elements and the extreme values are 2 and 3.
The Arithmetic mean will be the sum of all the elements and is divided by the number of elements in X. It is denoted by $ \overline{X} $ .
 $ \begin{align}
  & \Rightarrow \overline{X}=\dfrac{2+8+7+4+11+9+2+5+3}{9} \\
 & \Rightarrow \overline{X}=\dfrac{51}{9} \\
 & \Rightarrow \overline{X}=5.66 \\
\end{align} $
Thus, the mean is 5.66.
Now, we will increase the extremes 2 and 3 by 1 each.
Thus, new set will be X = {3, 8, 7, 4, 11, 9, 2, 5, 4}
 $ \begin{align}
  & \Rightarrow \overline{X}=\dfrac{3+8+7+4+11+9+2+5+4}{9} \\
 & \Rightarrow \overline{X}=\dfrac{53}{9} \\
 & \Rightarrow \overline{X}=5.88 \\
\end{align} $
The new Arithmetic Mean is 5.88.
As we can see, the mean doesn’t get affected much if we change the extreme values. The reason for this is that mean is based on addition of each value and each value in the data set has an equal effect on the Mean.
So, the correct answer is “Option C”.

Note: The extreme values of a data set don’t affect Mean much. When it comes to Median, the extreme values don’t have any effect, as mode is the central value of the data set. The Mode depends on the frequency of the values and any effect extreme values have will be only because of coincidence.