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Answer :
- In symmetric distributions, the mean and median are equal.
- The mean of the distribution is given as 170.
- Therefore, the median is also 170.
- The correct answer is $\boxed{170}$.
### Explanation
1. Understanding Symmetric Distributions
In a symmetric distribution, the mean and median are equal. This is a fundamental property of symmetric distributions.
2. Applying the Property
The problem states that the mean of the symmetric distribution is 170. Therefore, the median must also be 170.
3. Checking the Options
We examine the given options to find the value that matches the median we determined.
Option A: 210
Option B: 170
Option C: 150
Option D: 190
4. Final Answer
The only option that matches the median of 170 is option B. Therefore, the median of the distribution is 170.
### Examples
Understanding the properties of symmetric distributions is useful in many real-world scenarios. For example, when analyzing exam scores that are normally distributed (a type of symmetric distribution), the average score (mean) will be the same as the middle score (median). This helps educators understand the overall performance of students and identify areas where students may need additional support. Similarly, in manufacturing, if the dimensions of a product are symmetrically distributed around a target value, the mean and median dimensions will coincide, indicating consistent production quality.
- The mean of the distribution is given as 170.
- Therefore, the median is also 170.
- The correct answer is $\boxed{170}$.
### Explanation
1. Understanding Symmetric Distributions
In a symmetric distribution, the mean and median are equal. This is a fundamental property of symmetric distributions.
2. Applying the Property
The problem states that the mean of the symmetric distribution is 170. Therefore, the median must also be 170.
3. Checking the Options
We examine the given options to find the value that matches the median we determined.
Option A: 210
Option B: 170
Option C: 150
Option D: 190
4. Final Answer
The only option that matches the median of 170 is option B. Therefore, the median of the distribution is 170.
### Examples
Understanding the properties of symmetric distributions is useful in many real-world scenarios. For example, when analyzing exam scores that are normally distributed (a type of symmetric distribution), the average score (mean) will be the same as the middle score (median). This helps educators understand the overall performance of students and identify areas where students may need additional support. Similarly, in manufacturing, if the dimensions of a product are symmetrically distributed around a target value, the mean and median dimensions will coincide, indicating consistent production quality.
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