The combined mean of two groups $A$ and $B$ is $28$. The mean of group $A$ is $30$ when there are $25$ students in it. If there were $20$ students in group $B$, then what is the mean of group $B$?

Statistics

1. Facts or figures, collected with a definite purpose, are called data.
2. Statistics is the area of study dealing with the presentation, analysis and interpretation of data.
3. How data can be presented graphically in the form of bar graphs, histograms and frequency polygons.
4. The three measures of central tendency for ungrouped data are:

(i) Mean: It is found by adding all the values of the observations and dividing it by the total number of observations. It is denoted by $\overline{x}$.

So, $\overline{x}=\frac{{\displaystyle \sum _{i=1}^n}{x}_i}{n}$. For an ungrouped frequency distribution, it is $\overline{x}=\frac{{\displaystyle \sum _{i=1}^n{f}_i{x}_i}}{\sum _{i=1}^n{f}_i}$.

(ii) Median: It is the value of the middle-most observation (s).
If $n$ is an odd number, the median $=$ value of the ${\left(\frac{n+1}{2}\right)}^{th}$ observation.
If $n$ is an even number, median $=$ Mean of the values of the${\left(\frac{n}{2}\right)}^{th}$ and ${\left(\frac{n}{2}+1\right)}^{th}$ observations.

(iii) Mode: The mode is the most frequently occurring observation.