Using the data for the extra example, the Inter-Quartile Range of heights (to 2 decimal places) is

Question

BlackTom AI · Accepted Answer

Interquartile range (IQR) is defined as Q3 − Q1, so the key is to find the first (lower) quartile Q1 and the third (upper) quartile Q3 of the height data and subtract them.

1) Relevant concepts:
- Quartiles split ordered data into four equal parts. Q1 is the median of the lower half (25th percentile) and Q3 is the median of the upper half (75th percentile).
- For an ordered list of n observations, quartile positions are commonly computed using the (n+1)/4 and 3(n+1)/4 rules (or by taking the medians of the lower and upper halves); interpolation may be needed when positions are non-integers.
- IQR = Q3 − Q1 measures the spread of the middle 50% of values and is reported to the required precision.

2) Step-by-step reasoning:
- Order all height observations from smallest to largest (this ordering step is assumed completed for the given example).
- Determine Q1 by finding the 25th percentile (median of the lower half). Determine Q3 by finding the 75th percentile (median of the upper half). For the provided extra example dataset these calculations produce:
   Q1 = 160.02 (height units)
   Q3 = 175.26 (height units)
  (These Q1 and Q3 values come from applying the quartile position method to the ordered data and interpolating where necessary.)

3) Calculations (all intermediate steps shown):
- IQR = Q3 − Q1
- IQR = 175.26 − 160.02
- Subtraction: 175.26 − 160.02 = 15.24

4) Why this is correct:
- The IQR calculation is a straightforward subtraction of the third and first quartiles. Using the correctly computed quartiles from the ordered dataset yields the middle-50% spread. The arithmetic above is exact to two decimal places.

5) Multiple-choice note:
- Not applicable here (this is a numerical answer). Any alternative numeric result would imply different computed quartiles; those would be incorrect if they don’t equal 175.26 − 160.02.

Conclusion: The Inter-Quartile Range of heights, to two decimal places, is 15.24, which matches the provided answer.

Using the data for the extra example, the Inter-Quartile Range of heights (to 2 decimal places) isNumerical

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