Question

Find the mode of the data, using an empirical formula when it is given that \[median = 41.25\] and \[mean = 33.75\].

Answer 1

Hint: In the question as the values of mean and median is given, we can find the value of mode because of a relation between these three values for a given data set. For a data set the relation between mean, median and mode is given as \[Mode = 3Median - 2Mean\]. We can substitute the values of mean and median in the question and get the value of mode.

Complete step-by-step answer:
The mean for a data is given as 33.75 and the median is given as 41.25. As we know there’s a relation between mean, median and mode for a data, we will substitute the values of mean and median and get the value of mode.
We know that the relation between mean, median and mode is \[Mode = 3Median - 2Mean\]. For the data \[mean = 33.75\] and \[median = 41.25\]. Thus, on substituting these values, we get
\[
\Rightarrow Mode = 3Median - 2Mean \\
\Rightarrow Mode = 3(41.25) - 2(33.75) \\
 \Rightarrow Mode = 123.75 - 67.5 \\
\Rightarrow Mode = 56.25 \\
\]
Thus, the value of mode for the data will be 56.25.

Note: The relation between mean, median and mode is an established relation and students must be well versed with these formulae. Also the relation between mean median and mode is true for any set of data including skewed too. Mean is the average of the data, median is the middle value of data when arranged in ascending order and mode is the most frequent value in a data. The relation between these three cannot be derived but is based on observation, thus it is called an established relation.