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)At the beginning of an experiment, the birth weights of 60 Rattus norvegicus (laboratory rats) were measured. After the measurements were recorded, it was discovered that the scale was not accurately calibrated. The birth weights were adjusted to account for the incorrect measurements by adding 0.2 grams to each of the 60 weights. Which of the following statis-tics, calculated from the weights of the 60 lab rats, has the same value before and after the adjustment? I. The first quartile (Q]) II. The third quartile (3) III. The interquartile range (IQR) (A) I only (B) II only (C) III only (D) I and II (E) I, II and III

Question

)At the beginning of an experiment, the birth weights of 60 Rattus norvegicus (laboratory rats) were measured. After the measurements were recorded, it was discovered that the scale was not accurately calibrated. The birth weights were adjusted to account for the incorrect measurements by adding 0.2 grams to each of the 60 weights. Which of the following statis-tics, calculated from the weights of the 60 lab rats, has the same value before and after the adjustment? I. The first quartile (Q]) II. The third quartile (3) III. The interquartile range (IQR) (A) I only (B) II only (C) III only (D) I and II (E) I, II and III

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Solution

The answer is (C) III only.

Here's why:

I. The first quartile (Q1) - This would change because you are adding 0.2 grams to each weight, which would shift the entire data set up, including the first quartile.

II. The third quartile (Q3) - This would also change for the same reason as Q1. The entire data set is shifted up by 0.2 grams, including the third quartile.

III. The interquartile range (IQR) - This would stay the same. The IQR is a measure of statistical dispersion, or in other words, it's the range within which the middle 50% of the weights fall. It's calculated as Q3 - Q1. Since both Q1 and Q3 are shifted up by the same amount (0.2 grams), their difference (the IQR) remains the same.

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