for a frequency distribution of a variable mean=32 median=30. The distribution is

To determine the type of distribution given the mean and median of a frequency distribution, we can use the following general rules:

1. **Symmetrical Distribution:**
   - If the mean and median are equal (or very close), the distribution is approximately symmetrical.

2. **Positively Skewed Distribution:**
   - If the mean is greater than the median, the distribution is positively skewed (right-skewed). This implies that there are some higher values pulling the mean to the right.

3. **Negatively Skewed Distribution:**
   - If the mean is less than the median, the distribution is negatively skewed (left-skewed). This implies that there are some lower values pulling the mean to the left.

Given:
- Mean \(= 32\)
- Median \(= 30\)

Since the mean is greater than the median, the distribution is **positively skewed**.

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. How can you visually identify a positively skewed distribution on a histogram?
2. What are the characteristics of a negatively skewed distribution?
3. How does skewness affect the interpretation of the mean and median?
4. What are the common measures of central tendency and how are they affected by skewness?
5. How do outliers impact the mean and median in a skewed distribution?
6. What is the relationship between skewness and the shape of the distribution's tails?
7. How can you quantify the skewness of a distribution using statistical formulas?
8. What is the significance of the mode in a skewed distribution?

**Tip:** When analyzing skewed distributions, it's often useful to look at the median rather than the mean for a better representation of the central tendency, as the median is less affected by extreme values.

Explore the implications of mean and median values in a frequency distribution. Learn about skewness and its impact on distribution shapes. Suitable for advanced learners interested in statistics.

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