The marks obtained by 30 students of Class X of a certain school in a paper consisting of 100 marks are presented in table below. Find the mean of the marks obtained by the students. Marks obtained (xi) Number of students ( fi)
Step-by-Step Solution
Key Concept: For ungrouped (or discrete) data the mean \(\bar{x}\) is given by \(\displaystyle \bar{x}=\frac{\sum f_i x_i}{\sum f_i}\), where \(x_i\) are the observed values and \(f_i\) are their corresponding frequencies.
1. Write down the data
List each distinct mark \(x_i\) and the number of students \(f_i\) who obtained that mark.
2. Compute \(x_i \times f_i\) for each class
Multiply each mark by its frequency to obtain the total marks contributed by that group.
3. Find the sum of frequencies
\[\sum f_i = 30\] (given that there are 30 students).
4. Find the sum of \(x_i f_i\)
Add all the products obtained in step 2: \[\sum f_i x_i = (x_1 f_1)+(x_2 f_2)+\cdots+(x_k f_k)\].
5. Apply the formula for the mean
\[\bar{x}=\frac{\sum f_i x_i}{\sum f_i}=\frac{\sum f_i x_i}{30}\].
6. Calculate the numerical value
Substitute the value obtained in step 4 and evaluate the fraction to get the mean mark.
7. State the answer
The mean mark of the 30 students is \(\displaystyle \bar{x}=\frac{\sum f_i x_i}{30}\).
Correct Answer: Mean = (Σ fᵢ xᵢ) / 30