To find an approximation for the sample mean from the given grouped data, we use the formula for the mean of a frequency distribution:

$\text{Mean} (\bar{x}) = \frac{\sum (f \cdot x_m)}{\sum f}$

Where:

• $f$ is the frequency for each class.
• $x_m$ is the midpoint of each class (calculated as the average of the class interval).

Step-by-step calculation:

1. Class intervals and frequencies (already provided):

   • 0–4, 5–9, 10–14, 15–19, 20–24, 25–29, 30+

2. Calculate the midpoints $x_m$ for each class:

   • Midpoint of 0–4: $\frac{0 + 4}{2} = 2$
   • Midpoint of 5–9: $\frac{5 + 9}{2} = 7$
   • Midpoint of 10–14: $\frac{10 + 14}{2} = 12$
   • Midpoint of 15–19: $\frac{15 + 19}{2} = 17$
   • Midpoint of 20–24: $\frac{20 + 24}{2} = 22$
   • Midpoint of 25–29: $\frac{25 + 29}{2} = 27$
   • Midpoint of 30+: Since the class is open-ended, we approximate the midpoint as 32.

3. Multiply the frequency $f$ by the midpoint $x_m$ for each class.

Let me calculate the total for you.The approximate sample mean is $16.5$.

Do you have any further questions or would you like additional details?

Here are 5 related questions you might want to explore:

1. How do you calculate the median from grouped data?
2. What is the difference between a sample mean and a population mean?
3. How does changing class intervals affect the approximation of the mean?
4. How can we calculate the variance and standard deviation for grouped data?
5. What is the significance of using midpoints in frequency distribution?

Tip: In grouped data, the sample mean gives an estimate of the center of the data distribution, especially useful when the actual data values are not available.