How do I, find the estimated mean of that grouped data?


To find the **estimated mean** of grouped data using a frequency table, you can follow these steps:

### Formula for Estimated Mean:
\[
\text{Estimated Mean} = \frac{\sum (f \times x)}{\sum f}
\]
Where:
- \( f \) = Frequency of each group.
- \( x \) = Midpoint of each group.
- \( f \times x \) = The product of the frequency and midpoint for each group.
- \( \sum (f \times x) \) = The sum of all \( f \times x \) values.
- \( \sum f \) = The sum of all frequencies.

### Applying the Formula to Our Data:

#### Step 1: Sum of \( f \times x \) Values
From the completed table:
- \( \sum (f \times x) = 1 + 10 + 12 + 15 = 38 \)

#### Step 2: Sum of Frequency Values
- \( \sum f = 1 + 4 + 3 + 2 = 10 \)

#### Step 3: Calculate the Estimated Mean
\[
\text{Estimated Mean} = \frac{38}{10} = 3.8
\]

### Conclusion:
The estimated mean of the grouped data is **3.8**.

Would you like any more details or clarifications?

### 5 Related Questions:
1. How is the estimated mean different from the exact mean?
2. How can you use the estimated mean to compare data sets?
3. What is the effect of outliers on the estimated mean in grouped data?
4. How would the mean change if you added another group with a higher frequency and midpoint?
5. What is the relationship between the mean, median, and mode in a frequency distribution?

**Tip:** The estimated mean is particularly useful when dealing with large datasets where individual data points are not available, and only group frequencies are known.

Learn how to find the estimated mean of grouped data using a frequency table. Step-by-step guide with formulas and calculations included. Suitable for high school students studying statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation