Approximate the mean for following GFDT.
Data	Frequency
60 - 64	1
65 - 69	1
70 - 74	2
75 - 79	7
80 - 84	6
85 - 89	12
90 - 94	10
95 - 99	21
100 - 104	13
Report answer accurate to one decimal place.

To approximate the mean of the given grouped frequency distribution table (GFDT), we need to follow these steps:

### Step 1: Find the Midpoint (Class Mark) for Each Class Interval
The midpoint for each class interval is calculated as:
\[
\text{Midpoint} = \frac{\text{Lower Bound} + \text{Upper Bound}}{2}
\]

### Step 2: Multiply Each Midpoint by its Corresponding Frequency
Next, for each class interval, we multiply the midpoint by its frequency.

### Step 3: Sum the Products and Frequencies
We will sum the products and also sum the frequencies.

### Step 4: Calculate the Mean
The formula for the mean of a grouped frequency distribution is:
\[
\text{Mean} = \frac{\sum (f \times x)}{\sum f}
\]
Where:
- \( f \) is the frequency of each class,
- \( x \) is the midpoint of the class,
- \(\sum f\) is the total frequency.

Now, let’s go ahead and calculate it.

### Step 1: Midpoints

| Data Range | Frequency (f) | Midpoint (x) | f × x |
|------------|---------------|--------------|-------|
| 60 - 64    | 1             | 62           | 62    |
| 65 - 69    | 1             | 67           | 67    |
| 70 - 74    | 2             | 72           | 144   |
| 75 - 79    | 7             | 77           | 539   |
| 80 - 84    | 6             | 82           | 492   |
| 85 - 89    | 12            | 87           | 1044  |
| 90 - 94    | 10            | 92           | 920   |
| 95 - 99    | 21            | 97           | 2037  |
| 100 - 104  | 13            | 102          | 1326  |

### Step 2: Sum the Products and Frequencies

\[
\sum (f \times x) = 62 + 67 + 144 + 539 + 492 + 1044 + 920 + 2037 + 1326 = 5531
\]
\[
\sum f = 1 + 1 + 2 + 7 + 6 + 12 + 10 + 21 + 13 = 73
\]

### Step 3: Calculate the Mean

\[
\text{Mean} = \frac{\sum (f \times x)}{\sum f} = \frac{5531}{73} \approx 75.7
\]

Thus, the approximate mean for the given data is **75.7**.

---

Would you like further details or clarification? Here are some related questions for you to explore:

1. How do you calculate the variance for a grouped frequency distribution?
2. What is the difference between a grouped and ungrouped frequency distribution?
3. How does the median of a grouped frequency distribution differ from the mean?
4. How would you approximate the standard deviation from this grouped data?
5. What are some limitations of using midpoints in grouped frequency distributions?

**Tip**: When dealing with grouped data, always use the midpoint for each class interval, as it serves as a representative value for that interval.

Approximate the mean for the following GFDT.
Data	Frequency
60 - 64	1
65 - 69	1
70 - 74	2
75 - 79	7
80 - 84	6
85 - 89	12
90 - 94	10
95 - 99	21
100 - 104	13
Report answer accurate to one decimal place.

Learn how to approximate the mean for a grouped frequency distribution table (GFDT). This problem involves calculating midpoints, multiplying by frequency, and applying the grouped mean formula. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation