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Consider the data sets, which represent the amount of time, in minutes, it takes students to solve two logic puzzles.


Time (in minutes) to Solve Logic Puzzle
Which statement is true?

Responses

Logic Puzzle has a greater median and interquartile range than Logic Puzzle .
Logic Puzzle 1 has a greater median and interquartile range than Logic Puzzle 2 .

Logic Puzzle has a greater median than Logic Puzzle and an equal interquartile range to Logic Puzzle .
Logic Puzzle 1 has a greater median than Logic Puzzle 2 and an equal interquartile range to Logic Puzzle 2 .

Logic Puzzle has a smaller median and interquartile range than Logic Puzzle .
Logic Puzzle 1 has a smaller median and interquartile range than Logic Puzzle 2 .

Logic Puzzle has a smaller median than Logic Puzzle and an equal interquartile range to Logic Puzzle .
Logic Puzzle 1 has a smaller median than Logic Puzzle 2 and an equal interquartile range to Logic Puzzle 2 .
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1 answer

It seems that you are analyzing two data sets representing the time it takes students to solve two different logic puzzles (referred to as Logic Puzzle 1 and Logic Puzzle 2). To determine which statement is correct, you would typically need to compute the median and interquartile range (IQR) of both data sets.

Here’s how you can derive the necessary comparisons:

  1. Calculate the Median:

    • The median is the middle value of a dataset when it is ordered from least to greatest. If there is an even number of observations, the median is the average of the two middle numbers.

  2. Calculate the Interquartile Range (IQR):

    • The IQR is the difference between the first quartile (Q1) and the third quartile (Q3), which can be calculated as IQR = Q3 - Q1. Q1 is the median of the lower half of the data, and Q3 is the median of the upper half.

Once you have calculated the median and IQR for both puzzles, you will be able to evaluate the following statements:

  • Determine which puzzle has a greater median.
  • Determine which puzzle has a greater IQR.
  • Identify whether one puzzle's median is equal to the other's.
  • Identify whether one puzzle's IQR is equal to the other's.

Based on the results of your calculations, you can then select one of the statements provided.

Without actual numerical data for both puzzles, I cannot definitively tell you which statement is true. If you provide the data, I can assist you in calculating the median and IQR and help you identify which statement is accurate.