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How to Calculate Range and Interquartile Range from a Centipede Leg 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) is a graphical representation of a data set that 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 minimum and maximum values. It is used to visualize the spread and skewness of a data set.
2
Range of a Data Set
The range is a measure of spread that calculates the difference between the largest (maximum) and smallest (minimum) values in a data set. The formula is Range = Maximum Value - Minimum Value. It describes the total spread of the entire data set.
3
Interquartile Range (IQR)
The interquartile range is a measure of spread that focuses on the middle 50% of the data, calculated as the difference between the upper quartile (Q3, the value where 75% of data is below it) and the lower quartile (Q1, the value where 25% of data is below it). The formula is IQR = Q3 - Q1. It is less affected by outliers than the range, making it a more reliable measure for skewed data.
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