To calculate the arithmetic mean from the provided data, we need to use the following formula for grouped dataTo calculate the arithmetic mean from the provided data, we need to use the following formula for grouped

$\text{Arithmetic Mean} = \frac{\sum f_i x_i}{\sum f_i}$

Where:

• $f_i$ is the frequency (number of students).
• $x_i$ is the mark (class midpoints or given marks).

The data given in the image are:

Let's calculate the total for $\sum f_i x_i$ (the sum of the product of marks and students), and $\sum f_i$ (the total number of students). I will compute this now.The arithmetic mean of the marks is approximately 42.08.

Here's the breakdown:

• The total sum of the product of marks and the number of students ($\sum f_i x_i$) = 2020.
• The total number of students ($\sum f_i$) = 48.

Thus, the arithmetic mean is calculated as:

$\text{Arithmetic Mean} = \frac{2020}{48} \approx 42.08$

Would you like further details or clarifications?

Here are 5 related questions:

1. What is the difference between arithmetic mean and median?
2. How would you calculate the median from this data set?
3. What are some applications of the arithmetic mean in real life?
4. How would the result change if the number of students were different for each mark range?
5. How is the mode calculated for grouped data?

Tip: The arithmetic mean gives a good central value but is sensitive to extreme values (outliers). Consider using median or mode if your data has outliers.