In a symmetric distribution, Interquartile Range (IQR) = 10 and median = 10. Calculate the First Quartile (Q1)

In a symmetric distribution, the Interquartile Range (IQR) is evenly distributed around the median. Since the IQR is the difference between the Third Quartile (Q3) and the First Quartile (Q1):

\[
\text{IQR} = Q3 - Q1
\]

Given:
- IQR = 10
- Median = 10

In a symmetric distribution, the median is equidistant from Q1 and Q3, so:

\[
Q3 = \text{Median} + \frac{\text{IQR}}{2}
\]
\[
Q1 = \text{Median} - \frac{\text{IQR}}{2}
\]

Substituting the given values:

\[
Q1 = 10 - \frac{10}{2} = 10 - 5 = 5
\]

So, the First Quartile (Q1) is **5**.

Would you like more details or have any questions? 

Here are 8 related questions you might find helpful:

1. How do you calculate the Third Quartile (Q3) in a symmetric distribution?
2. What is the significance of the median in a symmetric distribution?
3. How does the IQR relate to the spread of data in a distribution?
4. How do you find the IQR in a skewed distribution?
5. What does it mean if Q1 is very close to the median?
6. How can you estimate Q1 if only the mean and standard deviation are known?
7. How would Q1 change if the IQR increased but the median stayed the same?
8. Can the median be higher than both Q1 and Q3? Why or why not?

**Tip:** The IQR is a measure of statistical dispersion, indicating the spread of the middle 50% of your data. It is especially useful for identifying outliers.

Learn how to calculate the First Quartile (Q1) in a symmetric distribution where the Interquartile Range (IQR) is 10 and the Median is 10. Understand the relationship between IQR, Median, Q1, and Q3 in statistical distributions.

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