The test score of 20 students are :
90, 60, 85, 100, 100, 90, 100, 75, 100,95, 95, 85, 30, 100, 40, 15, 100, 90, 70, 80
Number of students = 20
Mean : The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
[tex]\text{ Mean = }\frac{Sum\text{ of all data}}{Total\text{ number of data}}[/tex]
In the given question
Sum of all data = 90+60+85+100+100+90+100+75+100+95+95+85+30+100+40+15+100+90+70+80 = 1600
Sum of all data = 1600
Substitute the value in the expression of Mean :
[tex]\begin{gathered} \text{ Mean = }\frac{Sum\text{ of all data}}{Total\text{ number of data}} \\ \text{Mean}=\frac{1600}{20} \\ \text{Mean}=80 \end{gathered}[/tex]
Mean is 80
Mode : The mode is the number that occurs most often in a data set.
In the given data, frequency of each marks :
In the table, we can see that the maximum number of students has obtained 100 marks so
Mode = 100
Median : Median is the middle value of the set of the order Data
It express as :
[tex]\begin{gathered} \text{Median}=\frac{n+1}{2}^{th}\text{ when n is odd} \\ \text{Median}=\frac{\frac{n+1}{2}^{th}+\frac{n}{2}+1^{th}}{2}\text{ when n is even} \end{gathered}[/tex]
Arrange the data in the ascending order : 15, 30, 40, 60, 70, 75, 80, 85, 85, 90, 90, 90, 95, 95, 100, 100, 100, 100, 100, 100
n is the total number of terms :
as n = 20, which even so:
[tex]\begin{gathered} Median=\frac{(\frac{n}{2}^{th}+\frac{n}{2}+1^{th})\text{ Observation}}{2} \\ \text{Median}=\frac{(\frac{20}{2}^{th}+\frac{20}{2}+1^{th})\text{Observation}}{2} \\ \text{Median}=\frac{(10^{th}+(10+1)^{th})\text{Observation}}{2} \\ \text{Median}=\frac{(10^{th}+11^{th})\text{Observation}}{2} \\ Median=\frac{90+90}{2} \\ \text{Median}=\frac{180}{2} \\ \text{Median}=90 \end{gathered}[/tex]
Median is 90
Answer :
The mode 100
The mean 80
The median 90
