To calculate the average (mean) of grouped data using coding/AM (Aritmatika Modus) method, let's break down the steps:

Step 1: Identify the midpoints (Xi) for each class interval.

For each class, the midpoint is calculated as: $X_i = \frac{\text{Lower class limit} + \text{Upper class limit}}{2}$ Here are the class intervals and their midpoints:

1. $87 - 92$: $X_1 = \frac{87 + 92}{2} = 89.5$
2. $81 - 86$: $X_2 = \frac{81 + 86}{2} = 83.5$
3. $75 - 80$: $X_3 = \frac{75 + 80}{2} = 77.5$
4. $69 - 74$: $X_4 = \frac{69 + 74}{2} = 71.5$
5. $63 - 68$: $X_5 = \frac{63 + 68}{2} = 65.5$
6. $57 - 62$: $X_6 = \frac{57 + 62}{2} = 59.5$
7. $51 - 56$: $X_7 = \frac{51 + 56}{2} = 53.5$
8. $45 - 50$: $X_8 = \frac{45 + 50}{2} = 47.5$
9. $39 - 44$: $X_9 = \frac{39 + 44}{2} = 41.5$
10. $33 - 38$: $X_{10} = \frac{33 + 38}{2} = 35.5$

Step 2: Calculate $F_i \cdot X_i$

Now, multiply the midpoints by their respective frequencies $F_i$ (from the table).

• $F_1 \cdot X_1 = 1 \cdot 89.5 = 89.5$
• $F_2 \cdot X_2 = 2 \cdot 83.5 = 167$
• $F_3 \cdot X_3 = 0 \cdot 77.5 = 0$
• $F_4 \cdot X_4 = 13 \cdot 71.5 = 929.5$
• $F_5 \cdot X_5 = 10 \cdot 65.5 = 655$
• $F_6 \cdot X_6 = 8 \cdot 59.5 = 476$
• $F_7 \cdot X_7 = 8 \cdot 53.5 = 428$
• $F_8 \cdot X_8 = 7 \cdot 47.5 = 332.5$
• $F_9 \cdot X_9 = 0 \cdot 41.5 = 0$
• $F_{10} \cdot X_{10} = 1 \cdot 35.5 = 35.5$

Step 3: Sum $F_i \cdot X_i$

$\text{Sum of } F_i \cdot X_i = 89.5 + 167 + 0 + 929.5 + 655 + 476 + 428 + 332.5 + 0 + 35.5 = 3113$

Step 4: Calculate the total frequency $\sum F_i$

From the table, the total frequency is given as $\sum F_i = 50$.

Step 5: Compute the mean

The formula for the mean is: $\bar{X} = \frac{\sum F_i \cdot X_i}{\sum F_i}$ $\bar{X} = \frac{3113}{50} = 62.26$

Conclusion:

The mean value of the grouped data is approximately 62.26.

Would you like more details or further explanation?

Here are 5 related questions to deepen your understanding:

1. How would you calculate the mode for the same data set?
2. What if one of the class intervals had a different frequency, how would it affect the mean?
3. How can you determine the median from grouped data?
4. What is the significance of using midpoints in grouped data calculations?
5. How would the mean change if the intervals were smaller or larger?

Tip: When dealing with grouped data, always remember to compute the midpoints accurately, as they represent the values used in place of all the data points within each class.