Find the median marks in the data.

Marks	$15$	$20$	$10$	$25$	$5$
No of students	$10$	$8$	$6$	$4$	$1$

1. Representation of the Data:

(i) Representation of the data with actual observations with frequencies in a table is called ‘Ungrouped Frequency Distribution Table’ or ‘Table of Weighted Observations'.

(ii) Representation of a large data in the form of a frequency distribution table enables us to view the data at a glance, to find the range easily, to find which observation is repeating for how many times, to analyse and to interpret the data easily.

2. Measure of Central Tendency:

(i) A measure of central tendency is a typical value of the data around which other observations congregate.

(ii) Types of measure of central tendency : Mean, Mode, Median.

(iii) Mean is the sum observation of a data divided by the number of observations.

Mean $=\frac{\text{Sum of observations}}{\text{Number of observations}}$ or $\stackrel{-}{x}=\frac{\sum _{x_{\mathrm{i}}}}{n}$.

(iv) For ungrouped frequency distribution, arithmetic mean $\stackrel{-}{x}=\frac{\sum {\displaystyle f_{\mathrm{i}}}{\displaystyle x_{\mathrm{i}}}}{{\displaystyle \sum f_{\mathrm{i}}}}$.

(v) By deviation method, arithmetic mean $=A+\frac{\sum {\displaystyle f_{\mathrm{i}}}{\displaystyle d_{\mathrm{i}}}}{{\displaystyle \sum f_{\mathrm{i}}}}$, where $A$ is assumed mean and $\sum f_{\mathrm{i}}$ is the sum of the frequencies and $\sum f_{\mathrm{i}}{d}_{\mathrm{i}}$ is the sum of product of frequency and deviations.

(vi) Median is the middle observation of a data, when arranged in order (ascending / descending). 

(vii) When number of observations $‘n’$ is odd, median is ${\left(\frac{n+1}{2}\right)}^{th}$ observation.

(viii) When number of observations $‘n’$ is even, median is the average of ${\left(\frac{n}{2}\right)}^{th}$ and ${\left(\frac{n+1}{2}\right)}^{th}$ observations.

(ix) Median divides the data into two groups of equal number, one part comprising all values greater and the other comprising all values less than median.

(x) Mode is the value of the observation which occurs most frequently, i.e., an observation with the maximum frequency is called mode.$$