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Error Analysis  A student was asked to use the five boundary values to find the interquartile range​ (IQR). He incorrectly said the IQR is 142. Find the correct IQR. What mistake might he have​ made?

Minimumequals11​, First quartileequals54​, Medianequals82​, Third quartileequals110​, Maximumequals153
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Part 1
The correct IQR is
  
enter your response here.

1 answer

To find the interquartile range (IQR), you can use the formula:

\[ \text{IQR} = Q_3 - Q_1 \]

where \( Q_3 \) is the third quartile and \( Q_1 \) is the first quartile.

Given the values:

  • First quartile (\( Q_1 \)) = 54
  • Third quartile (\( Q_3 \)) = 110

Now, we can calculate the IQR:

\[ \text{IQR} = 110 - 54 = 56 \]

Part 1

The correct IQR is 56.

Possible Mistake

The student may have made an error in their calculation or misunderstood how to compute the IQR. Possible sources of error could include:

  1. Misinterpreting which values correspond to \( Q_1 \) and \( Q_3 \).
  2. Adding or subtracting incorrectly.
  3. Mixing up the formulas for finding ranges (such as calculating the range instead of the IQR).
  4. Failing to accurately identify \( Q_1 \) and \( Q_3 \) due to misdrawing a box plot or misunderstanding the position of the quartiles.

In this case, the student incorrectly calculated the IQR as 142, which suggests they either added another value incorrectly or didn't reference the quartiles accurately.