Question

What is the difference between the mean, median, and mode?

Answer 1

Mean: The mean is the ratio of the sum of all values to the total number of values in a data set.

Median: The median is the middle value of the data when the data is arranged in ascending or descending order.

1. When there are an odd number of terms in a data set, then the median is a ${\left(\frac{n+1}{2}\right)}^{th}$term of the arranged data.
2. When there are even number of terms in a data set, then the median is $\left[\frac{{\left({\displaystyle \frac{n}{2}}\right)}^{th}term+{\left({\displaystyle \frac{n}{2}}+1\right)}^{th}term}{2}\right]$, where $n$ is the number of observations

Mode: The mode is the most frequent number occurring in the data set.

For a data set: $2,4,3,4,5,6$

The mean of the data set is,

$Mean=\frac{2+4+3+4+5+6}{6}$

$\Rightarrow$ $Mean=\frac{24}{6}$

$\Rightarrow$ $Mean=4$

The median of the data set is,

arranged data set: $2,3,4,4,5,6$

$Median=\frac{4+4}{2}$

$\Rightarrow$ $Median=4$

The mode of the data set,

Mode is the most repeated number. So, the mode of data set is $4$.