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upper quartile

lower extreme

median

lower quartile

upper extreme

The image you have provided is a box plot (also known as a box-and-whisker plot). This plot visually represents the distribution of a data set by showing its minimum, lower quartile, median, upper quartile, and maximum.

Let's break it down:

- **Lower extreme (minimum)**: The smallest value, marked by the leftmost dot.
- **Lower quartile (Q1)**: This is the value at the 25th percentile of the data, marking the boundary between the lowest 25% and the next 75%.
- **Median (Q2)**: This value divides the data into two equal halves, marked by the line inside the box. It represents the 50th percentile.
- **Upper quartile (Q3)**: This value represents the 75th percentile of the data, indicating that 75% of the data is below this point.
- **Upper extreme (maximum)**: The largest value, marked by the rightmost dot.

From the image:
1. **Lower extreme** appears to be around 20.
2. **Lower quartile (Q1)** is approximately 40.
3. **Median (Q2)** is around 60.
4. **Upper quartile (Q3)** is around 70.
5. **Upper extreme** appears to be close to 90.

This box plot gives a clear picture of the spread of data, showing where the majority of data points fall and identifying any potential outliers (though none are indicated here).

Would you like further details or explanations about how these quartiles and extremes are calculated?

Here are 5 related questions to deepen your understanding:
1. How would you calculate the interquartile range (IQR) from this plot?
2. What does it mean if the box in a box plot is skewed to one side?
3. How does the median help in understanding the central tendency of data?
4. Can you identify any potential outliers from this box plot?
5. How would you compare this box plot with a histogram?

**Tip**: The interquartile range (IQR) is a useful measure of statistical spread and can be calculated as \( IQR = Q3 - Q1 \). It helps in identifying the range within which the central 50% of your data lies.

upper quartile, lower extreme, median, lower quartile, upper extreme

Learn how to interpret a box plot by understanding the lower quartile, median, upper quartile, and extremes. This problem breaks down key statistical concepts like the interquartile range (IQR) and data distribution. Ideal for students in Grades 6-8.

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