The problem asks to calculate the average height of students in a class based on the given grouped data.

Here is the frequency distribution table from the image:

To calculate the mean for this grouped dataThe problem asks to calculate the average height of students in a class based on the given grouped data.

Here is the frequency distribution table from the image:

To calculate the mean for this grouped

1. Find the class mark (midpoint) for each class interval.
   The midpoint for a class interval $[a, b]$ is calculated as: $\text{Class mark} = \frac{a + b}{2}$

2. Multiply each class mark by its corresponding frequency.

3. Sum all the values obtained in step 2.

4. Divide the sum by the total number of students (sum of frequencies) to find the mean.

Step-by-step calculation:

1. Class marks: $\text{For 150-156: } \frac{150+156}{2} = 153$ $\text{For 156-162: } \frac{156+162}{2} = 159$ $\text{For 162-168: } \frac{162+168}{2} = 165$ $\text{For 168-174: } \frac{168+174}{2} = 171$ $\text{For 174-180: } \frac{174+180}{2} = 177$

2. Multiply class marks by frequencies:

   $153 \times 4 = 612$ $159 \times 7 = 1113$ $165 \times 15 = 2475$ $171 \times 8 = 1368$ $177 \times 6 = 1062$

3. Sum of products: $612 + 1113 + 2475 + 1368 + 1062 = 7630$

4. Sum of frequencies: $4 + 7 + 15 + 8 + 6 = 40$

5. Mean height: $\text{Mean} = \frac{7630}{40} = 190.75 \text{ cm}$

The average height of the students is 190.75 cm.

Would you like more details or have any questions about the process?

Here are five follow-up questions to expand on this topic:

1. How would the mean change if another class interval was added?
2. What are the effects of outliers on the mean in a dataset?
3. Can you explain the difference between mean, median, and mode in grouped data?
4. How do you calculate the cumulative frequency for the above table?
5. What is the impact of varying class intervals on the accuracy of the mean?

Tip: For grouped data, the class mark helps simplify the process of finding the mean when dealing with intervals.