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Let's go over the questions and analyze them step by step.

### Question 1:
We have a set of seven observations: \(170, 125, 230, 190, 210, a, b\). The median is \(170\) and the mean deviation about the median is \(\frac{205}{7}\). We're asked to find the mean deviation about the mean of these observations.

The key steps would involve:
1. Calculate the mean of the seven observations.
2. Calculate the mean deviation about the mean.

However, the values of \(a\) and \(b\) need further steps to solve this.

### Question 2:
Given the mean and variance of data \(65, 68, 58, 44, 48, 45, 60, \alpha, \beta\) where \(\alpha > \beta\), and the mean and variance are \(56\) and \(66.2\) respectively, we're asked to find \(\alpha^2 + \beta^2\).

To solve this:
1. Use the mean formula to find an equation involving \(\alpha + \beta\).
2. Use the variance formula to find an equation involving \(\alpha^2 + \beta^2\).
3. Solve for \(\alpha^2 + \beta^2\).

### Question 3:
Given that the mean and variance of five observations are \(\frac{24}{5}\) and \(\frac{194}{25}\) respectively, and that the mean of the first four observations is \(\frac{7}{2}\), we need to find the variance of the first four observations.

We can use the following steps:
1. Let the five observations be \(x_1, x_2, x_3, x_4, x_5\).
2. Use the formulas for mean and variance to find the necessary relationships and solve for the variance of the first four observations.

### Question 4:
We need to find the median \(M\) of the given frequency distribution and then calculate \(20M\).

Steps:
1. Compute the cumulative frequency and find the median class.
2. Apply the median formula for grouped data.
3. Multiply the median by 20 to get \(20M\).

### Question 5:
We are given a table of data and asked to find the variance \(\sigma^2\).

To solve this:
1. Use the formula for variance: 
   \[
   \sigma^2 = \frac{\sum f_i (x_i - \bar{x})^2}{\sum f_i}
   \]
2. Calculate the mean \(\bar{x}\) and then the variance.

### Question 6:
The mean and variance of six observations are given, and we need to calculate \(a + 3b\).

Steps:
1. Set up equations using the given mean and variance.
2. Solve for \(a + 3b\).

### Question 7:
For the set of observations \(-3, 4, 7, -6, \alpha, \beta\), where the mean and variance are \(2\) and \(23\), we need to find the mean deviation about the mean.

Steps:
1. Calculate the mean using the given information.
2. Use the formula for mean deviation to compute the result.

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Would you like to go deeper into one specific question, or should I provide solutions for multiple? 

Here are 5 related questions based on this content:
1. How do you compute the mean and variance of grouped data?
2. What are the steps to find the median for a frequency distribution?
3. How do you derive the mean deviation from the mean of a data set?
4. Can the variance of the first four observations affect the overall variance?
5. How can you solve for unknown variables in a set of observations using the given mean and variance?

**Tip:** When working with frequency distributions, always compute the cumulative frequency first to simplify identifying the median class.

The image contains multiple math questions involving mean, variance, median, and mean deviation.

Explore detailed solutions to problems involving mean deviation, variance, and median for a given set of observations and frequency distributions. This guide covers key concepts such as calculating mean, variance, and solving for unknown variables.

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