vGroup

​10-under 20

​20-under 30

​30-under 40

​40-under 50

Frequency

55

77

99

44 approxiamte mean

To calculate the approximate mean for grouped data, we use the formula:

\[
\text{Mean} = \frac{\sum (f \cdot x)}{\sum f}
\]

Where:
- \( f \) is the frequency for each group.
- \( x \) is the midpoint of each group (also called the class mark).

### Step 1: Find the midpoints of each group.

- For the group "10-under 20": midpoint \( x_1 = \frac{10 + 20}{2} = 15 \)
- For the group "20-under 30": midpoint \( x_2 = \frac{20 + 30}{2} = 25 \)
- For the group "30-under 40": midpoint \( x_3 = \frac{30 + 40}{2} = 35 \)
- For the group "40-under 50": midpoint \( x_4 = \frac{40 + 50}{2} = 45 \)

### Step 2: Multiply each midpoint by its corresponding frequency.

- \( f_1 \cdot x_1 = 55 \cdot 15 = 825 \)
- \( f_2 \cdot x_2 = 77 \cdot 25 = 1925 \)
- \( f_3 \cdot x_3 = 99 \cdot 35 = 3465 \)
- \( f_4 \cdot x_4 = 44 \cdot 45 = 1980 \)

### Step 3: Sum up the products and frequencies.

- Sum of products: \( 825 + 1925 + 3465 + 1980 = 8195 \)
- Sum of frequencies: \( 55 + 77 + 99 + 44 = 275 \)

### Step 4: Calculate the approximate mean.

\[
\text{Mean} = \frac{8195}{275} \approx 29.8
\]

So, the approximate mean is **29.8**.

Would you like more details or explanations on any part of this?

Here are 5 questions for deeper understanding:
1. How is the midpoint calculated for each group?
2. What if the frequency distribution had more groups, how would it affect the mean?
3. How does this method compare to calculating the mean for ungrouped data?
4. What happens if the class intervals were unequal?
5. Can this method be used for non-numerical data?

**Tip**: Always ensure the intervals are consistent and the frequencies cover all data points for accurate calculations!

vGroup
​10-under 20
​20-under 30
​30-under 40
​40-under 50
Frequency
55
77
99
44 approximate mean

Learn how to calculate the approximate mean for grouped data using the formula Mean = (∑(f * x)) / ∑f. In this example, we compute the mean for frequency groups such as 10-20, 20-30, 30-40, and 40-50 with frequencies 55, 77, 99, and 44. Suitable for students in Grades 8-10.

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