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How to Calculate Range and Interquartile Range from a Centipede Leg Count 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 (end of left whisker), lower quartile (Q1, left box edge), median (line inside the box), upper quartile (Q3, right box edge), and maximum value (end of right whisker). 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, with a larger range indicating more variability in the dataset. Formula: Range = Max Value - Min Value.
3
Interquartile Range Calculation
The interquartile range (IQR) is a measure of the spread of the middle 50% of a dataset, calculated as the difference between the upper quartile (Q3) and lower quartile (Q1). It is less affected by outliers compared to the range, making it a more reliable measure for skewed data. Formula: IQR = Q3 - Q1.
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