Find the arithmetic mean of the following frequency distribution
x 140 142 150 148 145 147
f 4 1 2 1 2 2

To find the arithmetic mean of a frequency distribution, you use the formula:

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

Where:
- \( x \) represents the data values.
- \( f \) represents the frequencies of the corresponding data values.

Let's calculate this step by step:

### Step 1: Multiply each value of \( x \) by its corresponding frequency \( f \)
\[
140 \times 4 = 560
\]
\[
142 \times 1 = 142
\]
\[
150 \times 2 = 300
\]
\[
148 \times 1 = 148
\]
\[
145 \times 2 = 290
\]
\[
147 \times 2 = 294
\]

### Step 2: Sum the results of the products \( x \cdot f \)
\[
560 + 142 + 300 + 148 + 290 + 294 = 1734
\]

### Step 3: Sum the frequencies \( f \)
\[
4 + 1 + 2 + 1 + 2 + 2 = 12
\]

### Step 4: Calculate the arithmetic mean
\[
\bar{x} = \frac{1734}{12} = 144.5
\]

Thus, the arithmetic mean of the given frequency distribution is **144.5**.

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

Here are 5 related questions:
1. How is the weighted mean different from the arithmetic mean?
2. Can the arithmetic mean be used with non-numeric data?
3. How would the mean change if one of the values in the frequency table increased?
4. What is the role of the frequency in finding the arithmetic mean?
5. How can the arithmetic mean be misleading in some datasets?

**Tip:** When working with large datasets, organizing your calculations in a table format helps avoid errors and improves clarity.

Find the arithmetic mean of the following frequency distribution: x 140 142 150 148 145 147, f 4 1 2 1 2 2

Learn how to calculate the arithmetic mean of a frequency distribution using the data values: 140, 142, 150, 148, 145, 147 with corresponding frequencies. Follow the step-by-step solution, including the arithmetic mean formula and key statistical concepts. Suitable for students in Grades 6-8.

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