Question

The number of Science and Mathematics projects submitted by Model high school, Nandpur in last $20$ years at the state level science exhibition is:

$2,3,4,1,2,3,1,5,4,2,3,1,3,5,4,3,2,2,3,2$.

Prepare a frequency table and find the mean of the data.

Answer 1

The frequency table represents the frequency of each term in the given data. Therefore, the frequency table of the given data can drawn as:-

$\begin{array}{ccc}\text{Number of Projects}\left(x_i\right)& \text{Tally Marks}& \text{Frequency}\left(f_i\right)\\ 1& |||& 3\\ 2& |||||& 6\\ 3& |||||& 6\\ 4& |||& 3\\ 5& ||& 2\\ \text{Total}& & 20\end{array}$

Now to find the Mean of the data, we have to create one more column of $f_i{x}_i$.

$\begin{array}{ccc}\text{Number of Projects}\left(x_i\right)& \text{Frequency}\left(f_i\right)& f_i{x}_i\\ 1& 3& 1\times 3=3\\ 2& 6& 2\times 6=12\\ 3& 6& 3\times 6=18\\ 4& 3& 4\times 3=12\\ 5& 2& 5\times 2=10\\ \text{Total}& 20& 55\end{array}$

Therefore mean of the data is,

$\Rightarrow$ Mean $=\frac{\sum f_i{x}_i}{\sum f_i}$

$=\frac{55}{20}$

$=2.75$

Hence, the mean of the data is $2.75$.