Based on the provided image, which appears to be a promotional graphic for an educational resource on "Box & Whisker Plots," there is no specific mathematical problem to solve. The image showcases worksheets designed to teach and practice creating and interpreting box plots.
However, I can explain what a Box & Whisker Plot is and how to interpret one, using the information visible in the worksheets.
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What is a Box & Whisker Plot?
A Box & Whisker Plot (also known as a Box Plot) is a standardized way of displaying the distribution of data based on a five-number summary:
1.
Minimum: The smallest number in the data set.
2.
First Quartile (Q1): The median of the lower half of the data (the value below which 25% of the data falls).
3.
Median (Q2): The middle value of the data set (the value below which 50% of the data falls).
4.
Third Quartile (Q3): The median of the upper half of the data (the value below which 75% of the data falls).
5.
Maximum: The largest number in the data set.
The "box" represents the interquartile range (IQR), which is the range between Q1 and Q3. The "whiskers" extend from the box to the minimum and maximum values (excluding outliers).
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How to Interpret a Box & Whisker Plot (Using the Example Shown)
Looking at the worksheet on the left, we can see a completed box plot with a number line from 22 to 28.
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Minimum: The left whisker ends at
22. This is the smallest value in the data set.
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Q1 (First Quartile): The left edge of the box is at
25. This means 25% of the data points are less than or equal to 25.
*
Median (Q2): The line inside the box is at
26. This is the middle value; 50% of the data is below 26, and 50% is above.
*
Q3 (Third Quartile): The right edge of the box is at
28. This means 75% of the data points are less than or equal to 28.
*
Maximum: The right whisker ends at
28. This is the largest value in the data set.
From this, we can also calculate the
Interquartile Range (IQR):
IQR = Q3 - Q1 = 28 - 25 =
3
This tells us that the middle 50% of the data spans a range of 3 units.
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Example Statement Based on the Plot
As shown in the worksheet on the right, you might be asked to write statements like:
> "25% of the time, fewer than 25 bags of popcorn were sold."
This statement is true because Q1 is 25, meaning 25% of the data (days) had sales of 25 or fewer bags.
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In summary, while there isn't a single problem to solve, the image provides a clear visual guide to understanding the components of a box plot and how to extract meaningful information about a data set's distribution, central tendency, and spread.
Parent Tip: Review the logic above to help your child master the concept of fun box and whisker worksheet.
