Question

Which of the following cannot be determined graphically?
A. Mean
B. Mode
C. Median
D. None of these

Answer 1

Hint: In this problem we need to find the parameter which cannot be calculated by using the graph. So first we will list all the given parameters with their definitions. After that we will write the procedure to calculate each parameter for a given data set. From those procedures we can check which parameter cannot be calculated using the graph.

Complete step by step answer:
Given parameters are Mean, Mode, Median.
Let us first talk about the Mean. Mean is also called as Arithmetic Mean or Arithmetic Average. The name itself denotes that it is average value of the given data. Mathematically we can write it as the ratio of the sum of the observations to the number of observations. i.e.,
$\bar{x}=\dfrac{\sum{x}}{n}$
Where $\bar{x}$ is the mean, $\sum{x}$ is the sum of the observations, $n$ is the number of observations.
Now consider the parameter Mode. Mode is the variable or value which is repeated frequently in the given data. There is no formula for calculating the mode except observing the data.
When it comes to the parameter Median. It is the middle most term of the given data. So median can be calculated by
$\text{Median}={{\left( \dfrac{n+1}{2} \right)}^{th}}\text{ term}$ if $n$ is odd.
$\text{Median}=\dfrac{{{\left( \dfrac{n}{2} \right)}^{th}}\text{ term}+{{\left( \dfrac{n}{2}+1 \right)}^{th}}\text{ term}}{2}$ if $n$ is even.

We can observe that the parameter mean is calculated from the formula while other parameters are calculated by observing the data. So, when we have the data in graphical representation, we can easily find the values of median, mode by observing the graph. So, the mean cannot be calculated from the graph.

So, the correct answer is “Option A”.

Note: There is another parameter which is called a Range that also cannot be calculated from the graph. Range is defined as the difference between the highest values in the given data to the smallest value in the given data. So, it also cannot be calculated from the graph.