Answer :
Certainly! To find the mean of the given data, we can follow these steps systematically:
### Step 1: Understand the Data
We have two rows of data:
- Marks obtained: [tex]\( 20, 25, 30, 35, 40 \)[/tex]
- Number of students: [tex]\( 8, 10, 15, 8, 9 \)[/tex]
### Step 2: Calculate the Total Number of Students
We need to determine the total number of students, which is the sum of all the entries in the "Number of students" row:
[tex]\[ 8 + 10 + 15 + 8 + 9 = 50 \][/tex]
So, the total number of students is [tex]\( 50 \)[/tex].
### Step 3: Calculate the Sum of the Product of Marks and Number of Students
Next, we compute the sum of the products of each pair of marks obtained and the corresponding number of students. This can be done by multiplying each mark by the number of students who scored those marks and then summing all the products:
[tex]\[ \begin{align*} (20 \times 8) & = 160, \\ (25 \times 10) & = 250, \\ (30 \times 15) & = 450, \\ (35 \times 8) & = 280, \\ (40 \times 9) & = 360. \end{align*} \][/tex]
Adding these products together:
[tex]\[ 160 + 250 + 450 + 280 + 360 = 1500 \][/tex]
So, the sum of the products of marks obtained and number of students is [tex]\( 1500 \)[/tex].
### Step 4: Calculate the Mean
The mean can then be calculated by dividing the sum of the products by the total number of students:
[tex]\[ \text{Mean} = \frac{\text{Sum of the products}}{\text{Total number of students}} = \frac{1500}{50} = 30.0 \][/tex]
### Final Answer
The mean of the given marks obtained by the students is [tex]\( 30.0 \)[/tex].
### Step 1: Understand the Data
We have two rows of data:
- Marks obtained: [tex]\( 20, 25, 30, 35, 40 \)[/tex]
- Number of students: [tex]\( 8, 10, 15, 8, 9 \)[/tex]
### Step 2: Calculate the Total Number of Students
We need to determine the total number of students, which is the sum of all the entries in the "Number of students" row:
[tex]\[ 8 + 10 + 15 + 8 + 9 = 50 \][/tex]
So, the total number of students is [tex]\( 50 \)[/tex].
### Step 3: Calculate the Sum of the Product of Marks and Number of Students
Next, we compute the sum of the products of each pair of marks obtained and the corresponding number of students. This can be done by multiplying each mark by the number of students who scored those marks and then summing all the products:
[tex]\[ \begin{align*} (20 \times 8) & = 160, \\ (25 \times 10) & = 250, \\ (30 \times 15) & = 450, \\ (35 \times 8) & = 280, \\ (40 \times 9) & = 360. \end{align*} \][/tex]
Adding these products together:
[tex]\[ 160 + 250 + 450 + 280 + 360 = 1500 \][/tex]
So, the sum of the products of marks obtained and number of students is [tex]\( 1500 \)[/tex].
### Step 4: Calculate the Mean
The mean can then be calculated by dividing the sum of the products by the total number of students:
[tex]\[ \text{Mean} = \frac{\text{Sum of the products}}{\text{Total number of students}} = \frac{1500}{50} = 30.0 \][/tex]
### Final Answer
The mean of the given marks obtained by the students is [tex]\( 30.0 \)[/tex].
