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 (or average) of a frequency distribution, we use the formula:

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

Where:
- \( x \) is the value of the variable.
- \( f \) is the frequency of each value.

Let's calculate it 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 products of \( x \cdot f \).
\[
\sum (x \cdot f) = 560 + 142 + 300 + 148 + 290 + 294 = 1734
\]

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

### Step 4: Calculate the arithmetic mean.
\[
\text{Arithmetic Mean} = \frac{1734}{12} = 144.5
\]

The arithmetic mean of the given frequency distribution is **144.5**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the mean change if the frequency of \( x = 150 \) increased?
2. What is the median of this frequency distribution?
3. Can you calculate the mode for this data set?
4. How do you calculate the weighted mean for grouped data?
5. What is the difference between the arithmetic mean and the geometric mean?

**Tip:** When calculating the arithmetic mean of a frequency distribution, double-check the sum of frequencies to ensure accuracy.

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 the frequency distribution with x-values of 140, 142, 150, 148, 145, and 147, and corresponding frequencies of 4, 1, 2, 1, 2, and 2. Follow the step-by-step solution using the formula Σ (x * f) / Σ f to find the mean of 144.5. This guide is ideal for students in Grades 9-12 studying basic 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