Question

The marks obtained by 30 students in a class assessment of 5 marks is shown :
Marks
0
1
2
3
4
5

No. of students
1
3
6
10
5
5Find mean, median and mode of data.

Answer 1

Solution:

1) Calculation for Mean:

$\begin{table}[] \begin{tabular}{|l|l|l|} \cline{1-3} \begin{tabular}[c]{@{}l@{}}Observation\\ \\ \\ (x)\end{tabular} & \begin{tabular}[c]{@{}l@{}}Freq.\\ ( f)\end{tabular} & x f \\ \cline{1-3} 0 & 1 & 0 \\ \cline{1-3} 1 & 3 & 3 \\ \cline{1-3} 2 & 6 & 12 \\ \cline{1-3} 3 & 10 & 30 \\ \cline{1-3} 4 & 5 & 20 \\ \cline{1-3} 5 & 5 & 25 \\ \cline{1-3} Total & 30 & 90 \\ \cline{1-3} \end{tabular} \end{table}$

$Mean = \frac{sum \: of \: all \: observation}{total \: number \: of \: observation} \\ \\ = \frac{90}{30} \\ \\ Mean= 3$
2) Median:

Total number of observation n= 30

Since data is arranged in ascending order already

Find n/2 th term and (n/2 +1 )th term

Median is mean of 15th and 16 th observation

$\begin{table}[] \begin{tabular}{|l|l|l|} \cline{1-3} \begin{tabular}[c]{@{}l@{}}Observation\\ \\ \\ (x)\end{tabular} & \begin{tabular}[c]{@{}l@{}}Freq.\\ ( f)\end{tabular} & CF\\ \cline{1-3} 0 & 1 & 1 \\ \cline{1-3} 1 & 3 & 4 \\ \cline{1-3} 2 & 6 & 10 \\ \cline{1-3} 3 & 10 & 20 \\ \cline{1-3} 4 & 5 & 25 \\ \cline{1-3} 5 & 5 & 30 \\ \cline{1-3} Total & 30 & \\ \cline{1-3} \end{tabular} \end{table}$

11 to 20 observations are 3,

so 15th observation = 3

16th observation = 3

Median = (3+3)/2=3

3) Mode:

Mode is that observation which appears maximum time,from the table it is clear that,

Mode= 3

Hope it helps you.