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Calculate Range and Interquartile Range from a Centipede Legs Box Plot
Mathematics
Grade 9 (Junior High School)
Question Content
This box plot shows the distribution of the numbers of legs on some centipedes. Work out the range and the interquartile range of the numbers of legs.
Correct Answer
Range = 80, Interquartile Range = 40
Detailed Solution Steps
1
Step 1: Identify key values from the box plot. The minimum value (leftmost whisker) is 40, the maximum value (rightmost whisker) is 120, the lower quartile (Q1, left edge of the box) is 50, and the upper quartile (Q3, right edge of the box) is 90.
2
Step 2: Calculate the range using the formula: Range = Maximum Value - Minimum Value. Substitute the values: Range = 120 - 40 = 80.
3
Step 3: Calculate the interquartile range using the formula: Interquartile Range = Q3 - Q1. Substitute the values: Interquartile Range = 90 - 50 = 40.
Knowledge Points Involved
1
Box Plot Interpretation
A box plot (box-and-whisker plot) displays the distribution of numerical data. It shows the minimum value, lower quartile (Q1), median, upper quartile (Q3), and maximum value. The box represents the middle 50% of the data, with the left edge at Q1 and right edge at Q3, and whiskers extending to the min and max values. It is used to quickly identify the spread and central tendency of a dataset.
2
Range Calculation
The range is a measure of spread in a dataset, calculated as the difference between the maximum and minimum values. It represents the total span of the data, showing how far apart the highest and lowest values are. Formula: Range = Max Value - Min Value.
3
Interquartile Range (IQR) Calculation
The interquartile range is a robust measure of spread that focuses on the middle 50% of the data, calculated as the difference between the upper quartile (Q3) and lower quartile (Q1). It is not affected by extreme outliers, making it useful for skewed datasets. Formula: IQR = Q3 - Q1.
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