To calculate the mean and standard deviation from the given data, we need to follow these steps:

Data Extraction:

Class Intervals (Marks):

• $5-10$
• $10-15$
• $15-20$
• $20-25$
• $25-30$
• $30-35$
• $35-40$
• $40-45$
• $45-50$

Frequencies (No of Students):

• $7, 15, 24, 31, 42, 30, 26, 15, 10$

Step 1: Calculate the Midpoints

For each class interval, the midpoint $x_i$ is calculated as: $x_i = \frac{\text{lower limit} + \text{upper limit}}{2}$

Midpoints:

• $5-10$: $x_1 = \frac{5 + 10}{2} = 7.5$
• $10-15$: $x_2 = \frac{10 + 15}{2} = 12.5$
• $15-20$: $x_3 = \frac{15 + 20}{2} = 17.5$
• $20-25$: $x_4 = \frac{20 + 25}{2} = 22.5$
• $25-30$: $x_5 = \frac{25 + 30}{2} = 27.5$
• $30-35$: $x_6 = \frac{30 + 35}{2} = 32.5$
• $35-40$: $x_7 = \frac{35 + 40}{2} = 37.5$
• $40-45$: $x_8 = \frac{40 + 45}{2} = 42.5$
• $45-50$: $x_9 = \frac{45 + 50}{2} = 47.5$

Step 2: Calculate the Mean

The mean $\mu$ is given by: $\mu = \frac{\sum (f_i \cdot x_i)}{\sum f_i}$ Where:

• $f_i$ = frequency (number of students)
• $x_i$ = midpoints calculated above

I'll calculate this step-by-step now.The mean of the data is $\mu = 27.875$.

Step 3: Calculate the Standard Deviation

The formula for the standard deviation is: $\sigma = \sqrt{\frac{\sum f_i \cdot (x_i - \mu)^2}{\sum f_i}}$

Now, I'll compute this using the mean value obtained.It seems like I can’t do more advanced data analysis right now. Please try again later.

For now, the mean of the data is $\mu = 27.875$. If you'd like, I can guide you through the manual calculation of the standard deviation step by step, or you can provide another query for me to address.

Would you like to proceed with this, or do you have any other questions?

Here are some related questions you might consider:

1. How do I calculate variance manually?
2. What is the importance of standard deviation in data analysis?
3. Can the mean alone be enough to describe a dataset?
4. What other statistical measures are useful in interpreting frequency tables?
5. How does the choice of intervals affect the results of mean and standard deviation?

Tip: When dealing with grouped data, using midpoints simplifies the process of calculating statistical measures like mean and standard deviation.