
Find Variance  x² method 172,188,190,194,201,205,210,215,225,230,232,260

To find the variance using the \(x^2\) method, follow these steps:

### Given Data:
172, 188, 190, 194, 201, 205, 210, 215, 225, 230, 232, 260

### Step 1: Calculate the Mean (\(\mu\))

The mean is the sum of all the data points divided by the number of data points.

\[
\mu = \frac{172 + 188 + 190 + 194 + 201 + 205 + 210 + 215 + 225 + 230 + 232 + 260}{12}
\]

Let me calculate the mean.

\[
\mu = \frac{2622}{12} = 218.5
\]

### Step 2: Calculate \((x - \mu)^2\) for each data point

We now calculate the squared differences between each data point and the mean:

\[
(172 - 218.5)^2 = 2170.25
\]
\[
(188 - 218.5)^2 = 930.25
\]
\[
(190 - 218.5)^2 = 812.25
\]
\[
(194 - 218.5)^2 = 600.25
\]
\[
(201 - 218.5)^2 = 306.25
\]
\[
(205 - 218.5)^2 = 182.25
\]
\[
(210 - 218.5)^2 = 72.25
\]
\[
(215 - 218.5)^2 = 12.25
\]
\[
(225 - 218.5)^2 = 42.25
\]
\[
(230 - 218.5)^2 = 132.25
\]
\[
(232 - 218.5)^2 = 182.25
\]
\[
(260 - 218.5)^2 = 1736.25
\]

### Step 3: Find the sum of all squared differences

Now sum up all the squared differences:

\[
2170.25 + 930.25 + 812.25 + 600.25 + 306.25 + 182.25 + 72.25 + 12.25 + 42.25 + 132.25 + 182.25 + 1736.25 = 7180.5
\]

### Step 4: Divide by the number of data points (for population variance)

The variance is calculated by dividing the sum of the squared differences by the number of data points. For the population variance:

\[
\sigma^2 = \frac{7180.5}{12} = 598.375
\]

Thus, the **variance** is approximately **598.38**.

---

Let me know if you'd like more details or have questions.

### Relative questions:
1. How does variance differ from standard deviation?
2. How do you calculate variance for a sample instead of a population?
3. Can you explain why variance uses squared differences?
4. How is variance used in real-world data analysis?
5. What is the difference between population variance and sample variance?

### Tip:
When calculating variance, always ensure you're clear about whether you're working with a population or a sample, as this affects the denominator in the final step.

Find Variance x² method 172,188,190,194,201,205,210,215,225,230,232,260

Learn how to calculate the variance using the x² method for the data set: 172, 188, 190, 194, 201, 205, 210, 215, 225, 230, 232, 260. This solution explains step-by-step how to find the mean, compute squared differences, and derive the population variance. Ideal for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation